In playing Street Fighter 3 (3rd strike), I see the opponents blocking my attacks all the time so it doesn't do any damage. What buttons do I need to press to do this myself? (i.e high punch, med punch, up, down, etc.)
There are 2 types of blocking in SF3, the standard block, and parry.
The standard block is just to hold back or down+back to block high or low attacks, you will take some damage from special attacks this way.
The one that doesn't do any damage is most likely parry.
To properly parry an attack, you need to move into the attack at the moment the attack is about to hit you. Basically, push forward or down depending on if it is coming in high or low. If you time it right, you will parry the attack for no damage at all.
If the opponent is performing a normal attack move you on you (i.e. punch, kick, etc), they will be left open for a counter attack. If you parry a special (and yes even supers can be parried) then you will simply take no damage.