I'll give you a break down of what a typically first tournament experience is like.
Tournament matches are played in sets. Best of three until nearing the end of the bracket.
Here's how it usually goes down. After having showed up, paid the venue fee, and entered whichever events in which you're interested, you go around and play some friendlies, introducing yourself and getting to know everyone in the process.
Eventually, pools start. They're usually done in a round robin format. Groups of 4 to 8, depending on the turn-out, are assigned to their respective stations. Each person plays a set against everyone else in their group. I'll explain how the set works after. The people with the most wins make it out of the pools and get to play in the bracket.
The bracket stage is double elimination. The matches are called out, and you can usually ask to see the bracket or just access it on your phone. You find your opponent, introduce yourself if you don't already know them, and find an empty set up if one hasn't already been assigned to your match.
You both plug your controllers in and set up controls, toggle rumble, etc. Generally, from there, you both pick your character at the same time. Usually there's no issue to this, but sometimes a double blind pick has to be put in order. A similar thing applies to choosing controller ports, but neither of these scenarios are common, as far as I know.
Once the characters have been selected, you play rock paper scissors. This is to determine the order of stage striking. This is the process used to choose the starting stage. Every tournament has a starter or neutral list of stages that are considered to be reasonably fair. The number of stages is uneven. If the number of neutrals is five, then the first winner selects two stages they do not want to play on to strike. The loser then proceeds to strike two, leaving the winner to strike one of the two remaining stages, effectively choosing the stage.
Before starting a game, it's customary to say good luck and bump fists. Not necessary or anything, but yeah.
After the first match is played, it's up to the loser to choose a stage. On top of the list of neutral stages, there is also a list of counter-picks. These stages are not considered balanced enough to be neutral stages, but are fair enough to give characters a reasonable advantage in select match-ups. The winner of the match gets to ban a stage or two out of both lists, and then the loser picks the stage to play on. The winner then chooses their character, leaving the loser a character selection advantage, as well.
If the loser of the first match takes it, the counter-pick process is repeated. However, the winner of game 1 may not choose the stage they won on.
That's about it. If you do end up going to a tournament, make sure you read all the rules first. Be sure to play friendlies before the official start, and stick around after you're eliminated. Far too many new players leave after being knocked out, missing out on all the hype finals matches.