Magnet Rotate (around user-defined vector)
Magnet operations (updated for 0.98.16)
Overview - select geometry, define vector, choose influence radius of magnet, execute operation.

1). Select geometry to be scaled - I've chosen a 2 poly wide 'ring' all around the object.

2). Apply Face | Scale Radial  -> (Use RMB - Pick axis to scale out from). Choose a feature that provides a suitable axis for what you want to achieve. Since I want to do an eccentric radial scale, referenced to a 'corner edge' I've chosen the edge shown.
Use Alt + RMB on this edge to define the vector and access the magnet facility.

3). NB - Please note where the vector origin starts - this can be v. important for some ops. (although not here) - it's an edge midpoint in this case. (Try other elements, f / v and check the results - see vector page for more details about vector definition behaviour and associated origins/reference points)

4). Use RMB on the vert (shown) at one end to define the infuence radius and also execute  the command. Drag as required.

(To see the significance of the vector origin, undo all changes and try doing a Z scale with the vector defined in the same way as before. Note where the origin (0% scale) lies.)
Overview - select geometry, define vector, choose influence radius of magnet, execute operation.

1). Select faces to rotate (can be edges or verts)
Apply Face | Rotate (Use RMB option - Pick axis to rotate around) and also press Alt key (for accessing magnet option)
Here, I'll use the single vert (in the middle of the 4 faces) for defining the rotate axis. Picking this vert will give you the vert normal.

2).  RMB (on this vert) to select/define the axis AND move onto the next stage.(Could also define axis with LMB and then RMB to accept - you will have to do this if axis definition cannot be achieved by selecting a single geometry element - under these circumstances, using RMB can also be used to select the LAST element (of a sequence) necessary to define an axis - and continue the procedure.)

3). Wings now requires you to define the radius of influence (See info for [L] Pick outer boundary point for magnet influence)
RMB on a suitable piece of geometry to 'set' the required distance - in this case, I chose a vert 2 polys away (on the Z axis) from the nearest bit of selected geometry (shown as red square with blue edging)
(Using Alt + RMB at this stage would have provided magnet distance route options.)

4). Drag as required - finish executing command with LMB

Note the options displayed on the info line (bottom right of screen) - 4 different 'types' of magnet 'shape' and using +/- keys alters the magnet 'influence'. These options can be used whilst executing the command and Wings will update the geometry accordingly.
Overview - select geometry, define axis / vector, select origin point for vector axis, choose influence radius of magnet, execute operation

1). Select geometry to rotate and apply Face | Rotate -> (Use MMB option - Pick axis and ref point (to rotate through)). I decided on a vert on the Z axis to define the axis.

2).  Use RMB to accept this vert (vector displayed as blue arrow) - and continue with the procedure - ie moving this axis to act through another point.

3). Use Alt +RMB to pick a point thro' which you want the vector (parallel to original) to pass. (Here, I chose the lower RH corner vert of the selected geometry as the new 'origin / anchor point'.)
Using Alt with RMB also 'told' wings that I want to use magnets - as well as choosing a (single) element to define the new vector origin.
At this stage, both the vector (direction) and the new origin have been defined, so wings is now requesting that the magnet infuence radius be defined (see info line).

4). RMB on a suitable element (I picked a vert 2 edges away from the upper LH corner of the selected geometry - as shown) will not only define the magnet radius, but will execute the op.
(Using Alt + RMB at this final stage - will allow you to change the 'distance route' option)

5). Drag as required - the selection will now rotate around an axis that's parallel to the Z axis, but passing thro' the chosen point

As before, you can use +/- keys and / or change magnet type.
Overview - select geometry, choose axis, choose influence radius of magnet, execute operation

1). Select a vert on a grid (can be faces / edges) - I chose the centre one.
RMB for menu then LMB on Vert | Move (Along std. axis)

2). Use Alt + LMB to apply Vert | Move -> Y and to access magnet mode.
RMB on your chosen vert (the one on edge of grid) to select that vert and execute the op.

3). Drag as required. Changing the magnet type (keys 1-4) will produce obvious differences - Experiment
Magnet Rotate around a user-defined vector (through a chosen point.)
Wings lets you specify a particular origin for your rotate axis to pass through - this allows rotation of  geometry around any (selectable) feature on your model. (If you want to use a rotate axis that doesn't currently exist - create one, using a suitably orientated cube, or similar, as a 'reference block')
Magnet Move (parallel to a 'main' axis)
Magnet Radial Scale around a user-defined vector (through a chosen point)
Actual use of the magnet tools in Wings3D is really the only way to become familiar (and comfortable) with how they work. Reading info here (and elsewhere) will help, but there is no real substitute for 'hands-on' messing around and experimentation. After this, you'll have a much better 'feel' for their limitations and advantages. ie - what they can and can't do.

Familiarity will instil confidence and will fuel further experimentation with what is undoubtedly a very powerful range of geometry manipulators.

Note: Whilst this page deals with the magnet operations available with all supported tools, Tweak Mode also has a magnet option (press [1] to toggle on/off, see info line for radius, type and access options). Unlike the 'general' magnet modifier, TM magnet will only affect geometry being 'tweaked' ( moved) - not scaled, rotated etc - but is still a valuable addition.

Important factors to consider
The sometimes surprising, but rarely uninteresting, results you're likely to get from a magnet operation will depend on many factors:
Is a magnet op the best choice anyway?
Your model (shape / complexity - is there sufficient detail in the geometry to give a 'smooth' result?)
What geometry has been selected and how (shape of selection(s) and selection mode used)
Type of operation chosen (rotate / move / scale etc)
Location of the axis / vector being used (main xyz axis / translated through a user-defined point / user-defined vector / local / remote)
Influence radius (near /  far / infuence point on same or different object / purpose made object to provide influence point)
Type of magnet (shape) chosen.
Extent of +/- key usage.
Type of distance route chosen (wrong choice can affect surrounding geometry in an unwanted manner)
You - the user (how much you drag, assuming all the above is ok)

Having some idea of what you're trying to achieve, of course, also helps.

Magnet operations using vectors
Many of the examples used here incorporate a vector-based operation, rather than a 'standard' one associated with a main axis. Please read the info associated with vectors and their definition if further clarification is required  vectors
Overview - select geometry, define vector, choose influence radius of magnet, execute operation.

1). Create cylinder and select end to be manipulated.

2). Apply Face | Rotate -> (Use RMB option - Pick axis to rotate around)
Use Alt + RMB  to click on uppermost vert (shown). This action will choose the axis (defined by this vert) and access magnet options - see info line.

3). Use RMB on the same vert to define the magnet influence radius and execute the op.

4). Drag end face around to required position.

The above is a very basic sequence, as many things can be altered - picking a remote point (on other geometry?) for the rotate axis, for one - the type (and number) of elements chosen on the end of the rod, is another.
Magnet Rod bend around a user-defined vector (through a chosen point) - I'd suggest using the Vert | Bend tools if you want better bends (not in wings when I wrote this info.
A 'real' example of a magnet Scale op.
The requirement was to make an incomplete tube shape (in essence) with the top faces following a spiral type path.

1) Basic shape - select both circular edge sequences (top and bottom)
2) Dissolve these edges.
3) Select whole object
4) Cleanup (to get rid of stray verts - eyeball info display, top left to check)
5) Select one vertical end edge
6) Apply Edge | Scale Axis ->Y (RMB option - Pick point to scale from). Choose the lower vert of this edge - indicated by blue square.
Press Alt + RMB to specify this reference point and get the magnet option.
7) For defining influence radius, choose the vertical edge at the opposite end of the 'ring' (not shown)
Press Alt+RMB on this edge to display magnet distance route options - choose 'surface', Ok, and drag to suit. (Surface route option chosen here, as we want the 'magnetic influence' to 'flow around' the object being modified and smoothly change all intermediate geometry between the end edges - we don't want it to 'jump across the gap' and miss out the in-between geometry)
8) Select all inner (or outer) faces and apply Face | Extrude Normal to suit.
9) Finished object - note horizontal edges on top faces.

Magnet mode 3 (straight) was used - experimenting with the other (3) magnet options will produce different shapes that might also have been satisfactory - under different circumstances.

The approach shown here (producing a 'pattern') from which the final shape was extruded was used because of an issue with the upper radial edges when a straightforward Magnet Scale Y was used. (The top edges didn't stay parallel with the Y plane)
Magnet Scale (a real example)
main page
NB. To use Magnets and / or Vectors, it is essential to activate 'Advanced Menus' (Edit | Advanced prefs)

The procedures for accessing magnets and defining vectors have both been modified since this page was originally written -  the text here has now been amended to reflect these changes. (briefly outlined below)

Magnets are now accessed via a 'global switch' - ie, pressing the Alt key, together with the appropriate mouse button for the required command option. Pressing the Alt key, can be done at any valid stage (whenever you see 'Alt' in the info line) of the procedure - it doesn't necessarily have to be done at the start.

Greater use of MMB has been made, to separate the two main categories of workflow associated with user-defined vector definition procedure.
RMB now lets the user define just a vector axis, with no option for changing the (vector) origin from the default position determined by the elements used for axis definition. (The origin is at the base of the arrow that wings displays)
MMB provides the (2 step) facility to let the user (first) define a vector - and then (second) select a point, through which the chosen vector will pass.

With this (new) arrangement, the user can now opt for the RMB option, if they know they don't want the 'origin transfer' facility - and therefore not have to go through an unwanted / unecessary step.