Picking an inner tube size
Look at the tire. it will have a size on the sidewall. Something like 29" x something or 26" x something or 700/700c x something. Tubes are sold with a range of sizes like 700c x 20 mm - 25 mm. You just need to be within the range (or close to it).

Alternatively, you'll find a number like ISO/ETRTO 20-622. The 622 is the wheel size in ETRTO standard (in this case, 700c for common people), and 20 is the tire size. So the above 700 x 20-25 mm would work here.

I'd guess that you're running a 29er with a 22 mm rim width, so you'll need a 29" x something tube. 

Also, check the valve -- the common ones are presta (little screw you have to undo to pump) and schrader (like a car). You'll want to match this with the rim (use whatever is in the rim already).