Vertex Painter
Be sure the Skinning panel is expanded. (NOTE: This can be done within either the Setup or Animate tab.)
Select a bone (from the list or by directly clicking the object itself)
  Click the Edit button.
  The Vertex Painter will load, and you should see something similar to this:

If your interface appears slightly different, don't worry about it.
  The first thing I usually do after loading the Vertex Painter is expand the window by dragging the bottom-right corner, and click the Center Skin button.

Vertex Painter window after resizing and centering skin.
  Brief explanation of settings / functions:

RY - Rotates view along Y axis
RZ - Rotates view along Z axis
Zoom - Zooms in/out
Dot Size - Changes the display size of the vertices
Near / Far: Changes vertice display based on distance
Edges - Toggles display of edges(lines)
Bone - Toggles display of bone object
Reset View - Resets to default view
Center Bone - Zooms mesh so that selected bone is centered & takes up most of view
Center Skin - Zooms mesh so that all of mesh is in view
Auto - If enabled, Motion Studio updates the mesh object within trueSpace as it is being painted
Weight - If enabled, only vertices with existing weights will be affected (ie. white vertices will not be painted)
Size - Changes the size of the brush
Weight - Changes the weight of the brush (yellow is 'light' while red is 'heavy')
Paint - Paints the vertices with weight
Erase - Removes weight from the vertices
Blur - Blends weight based on weight of neighboring vertices
Soften -'Lightens' vertice weight

To pan the view, hold the right mouse button and drag.
If you have a mousewheel, this can control the Zoom.

  Go ahead and change your brush size. Notice that the green, circular cursor in the window is your brush, and reflects the size.

Click Erase and, using the left mouse button, drag over the painted vertices to erase their weights.
  Now drag the Weight slider until it is on the right(red) side and click Paint.
  Paint the vertices surrounding the selected bone.
  Now move to the next bone. To do this, simply select it from the list (you may keep the Vertex Painter open)
  Paint the vertices surrounding this bone, as you did with the previous one.
  Select the third bone and repeat the process.
  Move the Vertex Painter window to the side so that your object is visible. Drag a bone on your object and move it to see how the mesh deforms. NOTE: To update the mesh in the Vertex Painter, simply right-click.

  I will sometimes leave the object in a pose while adjusting the weights. This gives an immediate idea of how the mesh will behave.
  At this point you may begin with the fine adjustments of the vertex weights. To get smoother blending at the joints select a softer weight and start painting the neighboring vertices, or simply use the Smooth function.

Weights after Smooth operation on current bone
  Repeat the smoothing for each bone, if you like. Remember, you don't have to close the Vertex Painter window. Simply select a bone from the list or by clicking it directly within trueSpace.

Weights after Smooth operation on all bones
  It's easy to get carried away with the Smooth button. This is fine if you are animating a noodle, but for most cases you will only need to smooth the immediately-neighboring vertices. (ie. for human legs, arms, etc...)

Weights after several Smooth operation on all bones
  To reset your skeleton to the default / rest position simply change the animation time. You can do this by dragging the frame scrubber in trueSpace, or the one in MotionStudio.