Bicycle bottom bracket (crank hanger) shells fall, in general, into two groups, threaded and threadless. One-piece cranks fit only the unthreaded shells 51.3 mm (2.02") in diameter.
One-piece cranks are the easiest type to service, and require no special tools. All you need is a large adjustable wrench and a screwdriver.
Clean and inspect the cones, cups and bearing retainers. If they are smooth and free from pitting, you can re-use them. In most bicycle applications, bearings with loose balls are preferable to those that use retainers (cages.) One-piece cranks, along with headsets, are a major exception to this rule. It is extremely difficult to assemble a one-piece crank set with loose balls, I would not recommend trying.
Pedal threading is unique. One-piece cranks fit pedals with a 1/2" x 20 TPI threading. All other common cranks (except some older French cranks) use a 9/16" x 20 TPI threading. See my glossary entry on pedal threading.
There are two major types of one-piece crank sets, differentiated by their axle threading. The more common size uses 24 threads per inch, but some bikes, particularly older U.S. made Schwinn and Mongoose models, use 28 threads per inch. No part of the bearing assembly is interchangeable between threadings.cups are also a slightly different size internally, though they both fit the same frame bottom brackets. It is usually a good idea to buy a whole set (cones, cups, retainers) if there is serious wear to any of the parts. These are not expensive. Good sets are less than $20.
It is also possible to buy conversion bearing assemblies that will work with cotterless three-piece cranks. These are often worthwhile if you are trying to upgrade the performance of an older bike.
An even better solution is to get a set of adaptor bushings that permit the use of modern threaded cups and three-piece cranks.
A much wider variety of pedals is available for the pedal threading used on three-piece cranks..
You can also buy a spider or "power disc" that fits onto the one-piece crank as a normal chainwheel does, but which has holes to accept standard 110 mm or 130 mm BCD (Bolt Center Diameter) chainrings. This allows the use of high-quality 3/32" chainrings designed for derailer use. Most "power" discs will work with either the 110 mm or the 130 mm size.