Missing wood can be replaced only by a skilled woodworker. A botched repair is worse than no repair. However, small holes, chips, or cracks can be filled with a variety of fillers from the hardware store. Many come already stained; they are better to use. Although most of the "plastic wood" types are difficult to stain after hardening, they can easily be stained when the filler is partially dry.
Staining is a "feel" operation. It is mix and try. Penetrants such as the aniline dyes are quick drying but harder to work with in large areas, and have a fading problem in bright sunlight. The oil stains are better for those who have the patience to wait for them to dry.
If you can, try to keep from sanding the wood. If you must do so because of matching to a new piece, steel wool after sanding and then burnish to get the surface fibers to lay down. "Feather" the sanding, i.e., gradually sand outward from the affected area to prevent a noticable perimeter. When you stain to match, you will have to do the samething.
Unless you have some machining capabilities, or are willing to pay machine shop rates, you probably won't become involved in making metal parts. Some pieces can be made with a hacksaw and a file, but unless you are a craftsman, that's exaclty what they will look like. If you can make a new metal part, you'll have to get rid of that new look. Many solutions are available in paint stores and gun stores that will do this.
There are many books that will give you the rudiments of machining, blacksmithing and heat treating, if you wish to try some at home. There are, however, a few simple warnings worth mentioning. Cast iron parts usually break under shock (such as dropping on concrete). If you are lucky enough to find only a bent section of a cast iron part, don't try to straighten it. Even experts have difficulty with that. An area that you can do some good with is bent screws. If they are old and corroded, you'd be wiser to try to get them back as-is (if you choose not to replace them). If they have enough life left, heat them up to cherry-red before restraightening. They are far less likely to snap from "fatique" if you do this.
Collectors find that the easiest way to replace a missing part is to take one from a tool that is similar but in a worthless condition. There are a few warnings here. If the replaced part is from a model of another vintage, you have a bastardized piece. If it's a threaded part and the threads are slightly different (as many of them are), you can easily strip the treads trying to force in the wrong part. Good sense has to be used when cannibalizing. Needless to say, this is a very important point to look for when purchasing pieces that are susceptible to this practice, such as Stanley planes. There is also a question of personal eithics should you decide to trade or sell a piece that has had this type of repair.