Animation requires assigning meshes to Joints, then animating using Move/Rotate in the Anim mode.
To assign a mesh to a joint, first place the mesh on the grid (I'll use a plain 2x2 Box) then select the Joint button under the Model tab, now click on the grid somewhere. It will appear as a red sphere with multiple circles. Drag the joint into the box mesh and leave it there.
Now go to the Joints tab and select your joint (it will be called joint1 unless you changed its name) by double-clicking it, it shall turn red to signify that it is selected. Go to the Groups tab, and select your mesh (it should be called Box01 unless you changed its name), then go back to the Joints tab and press the Assign button.
Now that you've assigned the mesh to a joint, it's time to start animating.
To start, press the Anim button at the bottom right of the Milkshape 3D window. The vertices will disappear when you are in this mode. Now go and select your joint in the Joints tab, again it will appear red when it's selected. Once you've done that, head over to the Model tab and select Move.
To start, you will take a keyframe. First, click on the arrow at the bottom left of your window to make sure the current frame is set (no need to move it, just click once), then to take a keyframe, you can either go into the Animate tab (at the top left) and press the Set Keyframe button, or use the shortcut Ctrl+k to take 1 keyframe.
Now move the Arrow at the bottom left over to frame 2, then move the box in any direction you please, I'll use the Z-axis and go right 1 square. After the mesh has moved, take another keyframe (ctrl+k).
Repeat this process another time: Move Arrow Over 1>Move Mesh>Set Keyframe
Now, at the bottom right of your window, look for the button that signifies "Goto First Frame" and press it.
Click on the screen that shows the 3D view, and press the Play button.
If you did it right, you should see the box move two spaces to the right. A basic moving animation.
This same technique can be applied to models you've created. It gets a bit more advanced when doing these animations for Blockland (mostly just sequences).
