The first thing I'd look for is rear suspension. MTBs are pretty much the only bikes equipped with that. Next I'd look at the wheels. If it has wide, knobbly tires, odds are it's a MTB. This isn't 100% though, as there are narrow, smooth tires that'll fit a typical MTB rim as well.
Then I'd look at wheel size. Most common for MTBs is 26", AKA 559 mm. Wheel size will be written on the tire sidewall.
Next is the handlebars. MTBs will have either what's called a flat bar or a riser bar. What these two have in common is that the grip part will be pointing almost straight to the side. When you hold it your knuckles should be pointing forward. If the grip part is curved way back (with your knuckles turned pretty much sideways), then it's probably not a MTB.
Brakes: These days most MTBs will have disc brakes.
Frame: MTBs are meant to be able to take some abuse, or at least to look the part, so frame tubing on a new-ish bike will be thick and chunky.
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A good bmx bike will range from 20-25 lbs, have a small sprocket (cog) either 23 teeth, 25 or 28. It will also look nice have no or one break.
Unless you have experience and a good eye for sizes, read the wheel size of the tire sidewalls
Well, there is a look to them. 20" wheels, long, low frames. Handlebars look a certain way. Do a net search for bmx pics and you'll soon figure out what to look for.