Bicycle Tutor

Hello, I'm currently converting an old mountain bike to a single gear. I'm unsure of the appropriate wheel size to get. Is there a way I can measure and determine the size I need?

   
   

Are you sure that's a mountain bike?
MTBs usually have spigots for "cantilever brakes which that frame doesn't have. Wheel size will be either 26" or 700c. The size will initially be determined by the brake block position.
Personally I would expect that frame to have 700c wheels? If you can get hold of a wheel to try it out, either borrow or go to your local bike shop. There could still be different brake sizes required as the "drop" will be set by the distance that the wheel rim is from brake hole position in the forks and rear cross brace.
Before doing up a frame, cost out the parts as it is usually cheaper to buy a complete bike. (even a new one).

I honestly thought it was a moutain bike...but thats definitely a good point. I didnt notice that...Im gonna try 700c wheels. Thank you very much!!

It may have had 26" wheels. Some lower end mtn bikes used caliper brakes. That said, you may be able to fit 700 wheels on it if there is enough clearance. In fact, It'll be a faster bike with better braking with a larger wheel because you can use a shorter reach brake.
Singles are fun and I definitely encourage you to build something yourself. That said, don't drop too much on parts. This isn't a good frame and you can probably get a complete comparable bike and convert it for what you'd spend on buying a set of halfway decent new wheels.
$10 fixed gear conversion:
http://www.cicle.org/cicle_content/pivot/entry.php?id=1572