It's been a little while since I played, but here's what I remember:
- Use pneumatic weapons until you can get ahold of silenced revolvers/rifles. IIRC there's a Tihar (uses ball bearings) that can find relatively early on, and a Helsing (uses arrows) not too much later. Throwing knives are also very useful, because you can recover and reuse them, along with arrows, which is invaluable on harder difficulties (ball bearings, on the other hand, cannot be recovered. However, they are one of the cheapest types of ammo available). Throwing knives can also be used to stab using secondary fire, although if you're being stealthy enough to get close enough to stab enemies, you can just use the hunting knife.
- The sounds you make definitely matter. Crouching and moving slowly are a must, and pay attention to what you're walking on - certain materials (e.g., broken glass) are noisier than others, and tin cans can be hanging from the ceiling, specifically as a noise trap. Glass and cans will give away your exact location in a heartbeat.
- Light sources can be extinguished (candles and lamps can be blown out, lights can be shot or broken with your knife), but if you don't have NV goggles it can be more trouble than it's worth, because using a flashlight is a fantastic way to get yourself noticed. In addition, it can call attention to your location. If you're blowing out candles/lanterns, it's a good idea to vacate the area, because if an enemy notices they'll come check it out.
- Lines of sight and distance make a difference. Even in the pitch dark if an enemy is facing you and you're less ~8 feet away, you're going to get noticed. Try to stay behind enemies whenever possible.
- Height/altitude do help you hide, but you can still be seen. Hide in out of the way places, don't rely on a simple difference of elevation to keep you hidden.
Once you're spotted, you can definitely disappear again, but it's not necessarily easy (NB: once your presence is known, enemies won't 'forget' that someone else is around. You can hide, but they know you're out there somewhere). It's much easier to stay hidden than to hide again. Get in a dark, out of the way place, and don't move. The temptation to try to take out that single enemy who's searching in your area is very strong, but it will almost always result in you being found again. Stay hidden. Besides, the tension of waiting to see if your discovered or not is a great aspect of the game/immersion factor (one of the best features of the game, IMO).
Dead bodies will alert still living enemies. It's best to try to dispatch them in places that aren't patrolled frequently or at all. Approaching any new area, it's a good idea to wait and watch for a while. Figure out who goes where, and when, and plan your attack.
Re: levels of alertness, there are absolutely different levels of enemy awareness. Some are asleep. Some have searchlights. Some are engrossed in conversation, or interrogations. Some are non-aggressive until provoked. Generally speaking, it isn't too hard to figure out what's going to be more likely to discover you. A silently patrolling guard is looking for something suspicious (i.e., you). Others are busy doing other things.
Difficulty is of course a factor, particularly on the ranger/ranger hardcore (for the record, my favorite way to play the game) modes.
- You're more likely to be seen
- Once you're discovered, good luck surviving long enough to hide again
- If you can hide, enemies will keep looking for you for longer
All that being said, there's usually a non-aggressive route that you can take, frequently you can get through an area without firing a single shot. Stick to the shadows, move slowly and cautiously, and plan your actions. Locate good hiding spots. Be patient. And if all else fails, you can always start chucking grenades.
Fear the future, Metro dweller. Good luck.
(I'll fire up Metro 2033 again when I get the chance and see if there's anything that I missed, and it'll be good practice for Last Light.)
(Note: there's an option at some point to buy advanced armor, one style of which is stealth armor. However, I don't remember enough right now to definitively speak on that point, so I'm going to hold off on elaborating until I play through again)