what size bottom bracket do i have?

This is kind of tricky without taking it apart. There are also splined and and non-splined BB you need to take into account so your new BB will need to be compatible with your cranks. There are also special tools needed to install a BB. As a self proclaimed DIY guy it pains me to say, you should probably just take it to a bike shop to get this replaced. I just had this done on my bike after snapping the spindle (yes apparently that is possible after 10 years of hard riding) and it only cost slightly more to take it to the shop than to buy the parts and do it myself.

oh good one! if it's the same size as your mountain bike, then it's a euro-bottom bracket but if it's bigger, but not as big as your son's walmart brand bmx, then it's called a "Spanish Bottom Bracket" call the shop and tell them where you're at!