Just acquired a mountain bike and I believe it is a 24 inch. It needs new tires and inner tubes. I am trying to get the correct sizes.
24 inches is the diameter of the tires. The box on the replacement tubes should say 24 inches.
look on the tire. usually, it will be marked on the tire. or just get out some measuring tape and go from the top to bottom. if you want to make it difficult, measure the distance of the spokes and multiply by two.
The standard wheel size for mountain bikes is 26 inches. The width of the tire can vary, but it should be raised on the sides of the current tires - something like 26 x 1.75, as an example. Bicycle tubes usually support a range of widths, and can also usually go outside of the printed range, so it should be easy to find tubes. You will want to know if you need/want presta or schraeder valves - presta (or French) valves have a screw top and require an adapter if you use the air pumps at a gas station; schraeder valves are the same as car tire valves and work with the gas station pumps.
If you are primarily riding on street surfaces or on solid paths (crushed limestone, etc.) and not trail riding on loose dirt, you might want to get slick tires for your bike. Because they don't have the heavy tread, they feel much zippier on paved surfaces and are great for commuting.
If you don't plan to do the tire/tube replacement yourself, any decent bike store can find the right sized tires for you and tell you about slicks vs. treads.
The existing tires and tubes should have the proper size embossed on them. If you don't have them, just visit your local bike shop, they will be able to fix you up.
Look on the sidewall of the old tires. You will see numbers like 26 x 2.10 or similar. 26 is the tire diameter (26 inches) and 2.10 is the tire width in inches. If you see 24 x 2.00, you will need a 24 inch tire.