I know it's fun to start a game right away, but TAKE THE TUTORIAL. Use the roll button to turn 180 degrees. Turning around on foot is too slow. By the way, did you know you could roll by pressing forwards and backwards really quickly on the keyboard? I sure didn't. Thanks to Jarrod Selsmark of Australia I do now. You can never screw up and get stuck somewhere. If you're alive, there's a way to finish the level. (Okay, someone found one exception. Don't drop into the room with the spikes when the water isn't raised in the Cistern.) Be conservative with your health early on. There is all sorts of medic kits laying around these levels. Later in the game, you'll have so many health packs that you can be much more bold. If you're coming to the very end of a level, don't waste medicine by healing yourself. You're automatically healed at the end of the level. If you're stuck, it's usually because you didn't look around enough. Revisit all rooms you have access to and give them a good staring down. You'll notice on my controls page that I set up one of my gamepad buttons as a save button. Man, I love that button.
Jumping
Learn what jump is good for what. The tutorial helps a bit on this, but you need to play a while before you can gauge distances well. Jumping distance goes in this order (from shortest to longest): back flip, standing jump, side jump, running jump. There are some ledges you can only reach with a side jump, oddly enough. If you jump onto a sloped surface and hit the jump key right when you make contact, you'll bounce off of the surface and get a lot higher than you would with a normal jump. You will always go perpendicular to the surface, so it doesn't matter what the original angle was. Thanks to Paul Potiki of New Zealand for reminding me that holding action while jumping will increase the length of your jump whether or not you try to grab a ledge. I ran a little test jumping off a ledge onto a gridded floor. I got an extra foot's length by holding down action. Never give a ledge a long run-up. It doesn't help and it messes up your timing. Just walk to the edge, hop back, run and jump. Works perfectly every time.
Fighting
Don't run around with your guns in your hands. Most of the time you can climb your way out of danger rather than shoot your way out. If you're on a ledge shooting at something that can't get you, use the pistols (duh). In tight spots where you suspect something is coming (like in any tight area in the Egypt levels), keep the bigger weapons handy. You can draw while you're flipping the air. Not only do you avoid damage while you do it, it looks sooo cool. Don't forget you can heal at any time. You can survive nearly any attacks this way. Don't worry about realism, life is more important. :) Unless you're at the end of a level, don't stand there and have a shoot out with another human (up until Natla's Mines). He'll stand there all day and shoot you. Give him a few shots then turn around, he'll dissappear. Yes, you can be shot while swimming. You can't fire from the water, though. If you ever find yourelf aiming with one hand, swivel until both are firing . It only makes sense. If you know there are enemies on a level below you, but they won't come out so you can shoot them, turn around and hang on a ledge. They'll come out and wait for you to drop. Simply climb back up and start shooting. (Thanks to Scott Harrison of the USA for reminding me of this.)
Swimming
Always keep track of where you were so you can head back to a surface you know of. Many times it is better to stay in one place and pivot to pick a direction rather than to keep swimming. Pick a "stuck direction" for when you get stuck in a corner. For example, decide to always turn left if you get stuck. That way, you can turn out of tight spots without losing your orientation. Don't try to get around much on the surface. Underwater swimming is several times faster. You can be shot while in the water, but cannot use your own weapons. Alligators do a lot of damage, but they are fairly easy to avoid. Most of the time, it's a head-on situation. Swim high in the water then dart down suddenly right before you meet. He doesn't change directions very quickly. Remember, sharp turns. If you want to do something really funny (I did this but I had to because I got lost like an idiot), let your air run out and see how long your health packs will keep you alive. You may have to burn several of them, but it can save your life. It takes good timing to use one every few seconds and keep swimming.
Special Moves
There are two really cool moves in the game. Most people know about the first one:
1. Swan Dive/Roll - Jump+Walk+Forward. This looks so cool. My saved games page has a really cool example of a chance to dive several stories. When you do it on the ground, you roll out of it.
2. Hand Stand - While hanging, Action+Walk+Forward (hold). I read this on somebody's page and tried it right away. I think it's the coolest thing Lara does. She does a hand stand, then pulls her legs over one at a time. Once her first leg goes down, the one that is still up bobs to the center to let her keep her balance. I was very impressed.