Explain to me like I'm 5

so when you open the tournament page you will see something like this.

the numbers are the first thing to know. the first number is the amount of time you have in the game. the second number is the increment (in seconds). for example 30l0 means it is a 30 minute game with 0 increment. 2l1 means it is 1 minute, with 1 second increment. 

right after the number you will see what kind of game mode it is. bullet, blitz, and rapid are all time controls for a normal game of chess. This is what you should stick to if you want a normal game of chess. stuff like "king of the hill", "crazyhouse", "bughouse", "960", etc, are variants of chess. stay clear of the variants if you want to play a normal game of chess.

the next word(s) is going to be the type of tournament. This tells you the format of the tournament. if it is swiss, that means there is going to be a set amount of rounds. Each player plays a game in a round. and whoever gains the most points at the end of all the rounds wins. arena is slightly different. arena means the tournament starts and ends at a set time, and after that set time whoever has the most points wins. there are no rounds in arena tournaments, when you finish a game, you can start a search for the next game. 

you will sometimes see something like (1500+) or (U1200). This is jsut telling you the rating range that are permitted in playing in the tournament. U means under. + means more.

Ok. Thank you so much, this really clarifies things.

Follow up question-when you say "increment" what does that mean?

increment is after you make a move your gain that much time in seconds. so for example in a 15l10 game. you have 15 minutes to play, and each move you make you gain 10 seconds more to play with.

To clarify Chess_Player_lol's point, only the clock on your end will be increased by the said increment after your move - your opponent will not gain any time for it.

Conversely, your time will not increase after the conclusion of your opponent's move.

The standard rules (loss on time, loss by checkmate etc) continue to apply as usual for standard games of chess (excluding the variants).

So for example, in a 3|2 game (3 minutes per side, with 2 seconds increment after a completed move), the game could go like this (if I recall, the first move each by White and Black does not consume any time at all).

1. e4 (White moves instantly; White 3:02, Black 3:00)

1..e5 (Black responds instantly; White 3:02, Black 3:02)

2. Qf3 (White takes 1 second to move; White 3:03, Black 3:02)

2...a5 (Black takes 5 seconds to move; White 3:03, Black 2:59)

3. Bc4 (White takes 10 seconds to move; White 2:55, Black 2:59)

3...a4 (Black takes 2 seconds to move; White 2:55, Black 2:59)

4. Qxf7# (at this point the game ends, so the timer stops)

@5, @6
The increment is added before the move, not after.

"increment: 6.1. An amount of time (from 2 to 60 seconds) added from the start before each move for the player. This can be in either delay or cumulative mode."

https://handbook.fide.com/chapter/E012018 

i'm pretty sure on chess.com it is after. though that is such a small detail that I wouldnt have noticed.

@8
Yes. It is an incorrect implementation.
The increment should be added before per Laws of Chess and that enables time controls like 0|2.

On some other sites I have played (not the seven-letter one), the increment starts before, so that each player starts with exactly 3 minutes on their first move in a 3|2 game - and if one player does not make a move, his timer can run out (I can't remember whether there was any abandonment rules on that site or not).

This site only starts the timer proper after each player has made a move - but the increment takes effect as usual, so technically each player starts with 3 min 2 sec instead of 3 min in a 3|2 game.

Troglodyte. 

Cool