I solve the problems on chesstempo.com (which is a great site for tactics by the way) on a regular basis. The first thing I do is look for anything unusual (pins, potential skewers, removal of defending pieces). As the solver, you're already aware that the opponent has made a slight (or sometimes obvious) miscalculation in regards to tactics. If I see that the king is rather vulnerable, I try to imagine my pieces in certain squares that would allow for a checkmate. Imagine them in an ideal position. Then think of a way of getting them there. Also, when you see a very obvious tactical mistake, look twice as it may either be a trap or your opponent's desperate attempt of getting out of a forced-mate position.
Be sure to take as much time possible to think of which moves you would like to play and try to replay all possible variations in your head as this will also train you to visualize in chess; only move when you are 100% sure of your answer.
I just recently got ct-art 3.0 and am really excited to improve my tactics. I am ready to commit myself to doing a lot of tactic problems, and I now just need some help with solving them correctly. Could anybody explain the thought process behind solving tactic problems? Do you pretend like it's a normal game, and look at your opponents checks captures and threats before you look for a tactic? Or do you just look for a tactic as soon as you see the problem? Do you evaluate the position at first to see who has the better position?
Any comments at all would be appreciated, thanks.