Saab,
I agree completely with FNG's description of how to go around from either downwind or base.
Jayemm,
As FNG said, don't be too harsh on yourself. Something to consider, though (and it may or may not have been appropriate or possible in this situation, I don't know...) is having a quick chat with the other pilot in the club-house afterwards - just to clear the air, make sure that he knows that you know that you didn't make the best choice, and doesn't walk away calling you an a$$-hole when all you've done is make a minor mistake.
(Happened to me last weekend, in fact. I was joining from the deadside, when someone took off and announced they were turning downwind for a low-level circuit. I realised there was a potential conflict, and decided to fly a tight circuit myself to stay ahead of the other aircraft. I completely screwed it up - the other aircraft was much tighter than I was, and I actually made the conflict worse. The other pilot informed me that he wanted to go in front of me, which was fine by me, so I extended downwind - but I think we were both left wondering what the other one was thinking. On the ground, though, we had a brief chat and both walked away knowing that both of us could have handled the situation better, and both of us were aware of our mistake, therefore neither of us was calling the other an a$$-hole. And, what's more, the other pilot turned out to be an examiner who was just finishing a successful skills test with another PPRuNer - so congratulations, you know who you are!
)
FFF
----------------