The vertex painter displays the skinned mesh in a special wireframe view, and provides various controls for editing skin weighting.

The right side of the vertex painter holds the vertex view. This display shows a wireframe view of the skinned object.
Vertices closest to the camera are largest and brightest. Use the Dot Size control to adjust the vertex size on the display.
Vertex weighting is shown by color. Red vertices are selected and are most heavily influenced by the bone, orange are somewhat influenced, yellow vertices are less influenced, and white vertices are not selected at all.
By clicking on the vertex display and dragging the brush circle, you can paint weights onto vertices. Unweighted vertices are not affected by the bone. Weighted vertices are affected by the bone on a sliding scale, with heavier weighted vertices being affected the most (and lighter the least).
Several brushes are provided so that the mouse is used to paint weights onto vertices.
Note: weighting only applies to vertices that are shared by more than one bone. In this case, the weights are used to blend the bone influences together. If only one bone is controlling a vertex, it always has 100% influence, regardless of the vertex weight.
You can use the mouse to manipulate this view.
You also use the mouse to paint weights onto vertices.
There are also some shortcut keys.
The wireframe view has near and far clipping planes to help you isolate the vertices you wish to paint. Vertices farther from the camera than the far plane are hidden. Vertices closer than the near plane are hidden. By default, the painter opens with the far plane set at half the depth of the model (0.5) and the near plane set all the way in front (1.0, hiding no vertices).
The RY and RZ spinners will rotate the mesh around the Y and Z axes. The Zoom spinner changes the scaling of the display.
The vertex painter has it's own undo/redo buttons and collapsable control panels.

Dot Size controls the drawing size of vertex dots in the wireframe display.
Near sets the distance to the near clipping-plane. Vertices closer to the camera than the near clipping-plane are hidden. Value of 1.0 is nearest the viewer, 0.0 is farthest.
Far sets the distance to the far clipping-plane. Vertices farther from the camera than the far clipping-plane are hidden. Value of 1.0 is nearest the viewer, 0.0 is farthest.
The Edges button toggles the display of edges in the wireframe display. Bone toggles the display of the bone.
Click Reset View to set the wireframe view to match the active trueSpace view.
Center Bone zooms and pans the display so that the selected bone is centered and fully visible (zoom extents). Center Skin zooms so that the entire skin is visible.
Click Apply to update the skin object with any changes made in the vertex painter. You rarely have to click this button, as usually you will be using an auto-apply Brush (see below).
Click Refresh to copy the vertex information from the skin object to the vertex painter display. This is the opposite of Apply, and you will lose any unapplied changes in the vertex painter.
The Smooth button applies a smoothing filter to all vertices. The smoothing filter will cause your selected area to spread out smoothly over the object. Smoothing operations are not automatically applied, and can be undone.

When Auto is enabled, changes made with the brush are automatically applied to the skin object.
If Weight is on, the brush will only affect vertices that are already weighted. No new vertices will be painted.
Size controls the size of the brush.
Weight controls the weight that is painted with the Paint brush (left is lightest, right is heaviest).
The Paint, Erase, Blur, and Soften buttons are used to select a brush type. Only one brush type is selected at a time.
Erase completely removes weighting from all vertices under the brush.
Blur blurs the weighting of vertices under the brush. The blur is accomplished by averaging the weights of vertices that are connected by edges.
Soften reduces the weight of vertices under the brush. The more times a vertex is painted with the soften brush, the lighter the weighting becomes until the vertex is finally completely unweighted. Hold down Ctrl while using the Soften brush to make vertices heavier instead of lighter.