DON'T: Take offense to a bad mood. If the guys your man is rooting for aren't exactly turning in a stellar performance, he might be a little surly. Don't take offense if he's a bit snappy if you ask a question just after a heated moment in the match, or if screams at the TV—as if every single player can hear him. This happens frequently, and is just another part of the game. No worries. He will soon be back to normal.
DO: Soak it all in. I had a dad and brother who taught me a lot about sports, but I was able to learn a ton just by observing. You can, too! So, sit back and take it in. You'll catch onto any game pretty fast if you watch enough, and take note of recurring or rare plays; like in basketball, it's a travel if a guy takes an extra step without dribbling; in football, it's a safety if a player is tackled in his own end zone; in hockey, it's icing if a player sends a puck past two red lines... Soak up knowledge on your own, and you'll eventually be impressing your guy on a regular basis with your own insights on the game.
Do you like watching sports with your guy or do you retreat to a "girl cave?"