Prior to doing the motor work, remove it from the machine. If the wiring is rotted, cut it off to ease the removal of the wiring - the excess will be pulled through the motor casing later on. You may want to save the 2 prong plug for reuse - often the older sewing machines will have plugs that are composite rahter than a molded unit which makes reuse possible.
Once the motor is removed, there's typically 2 long bolts holding the twp parts of the casing together. the nuts securing the end of the bolts need to be removed so the 2 parts can be eased apart. I think there are around a 8mm or 9mm nut typically.
In addition to removing the nuts, the belt wheel will need to be removed from the motor shaft. this is usually just secured with a clamp bolt that clamps the wheel onto the shaft. It can be removed simply by backing the securing screw out a little bit.
Once the nuts and the wheel are removed, the two parts of the motor casing can be eased apart. Usually it's a good idea to do this pretty gently. Another optional step which can be taken prior to separating the casing parts is removing the brush springs and brushes. this is done by backing out the spring retainers with a flathead screwdriver. I don't have an image of this, but it's probably not a bad idea.
With one side of the casing removed, the other side can be removed from the internal motor parts as well. You can see from the image below that there can be ALOT of debris in the motor - it's not a bad idea to do this work over some workspace that can be easily cleaned. Basically at this point there will be the 2 sides of the motor casing and the main motor internal. The wiring will be pulled through a hold on one part of the casing and eased through the hole as the appropriate side of the casing is removed.
With the parts all pulled, you can get to any number of parts. Usually I'll blow out the motor, clean off any corrosion that may be on the coil wraps, redo the wiring, replace the brushes and regrease everything. If you have questions on any of these, let me know and I'll add another post with additional detail.