Every season, you must play 10 qualifying matches in a playlist to obtain a rank for that playlist. Ranks are determined from a mix of your performance in qualifying matches and your final rank of the previous season (if applicable). Ranks reset every season (every 2-3 months or so, can’t remember for sure).
Ranks are divided in tiers, from lowest to highest:
Bronze 1-6, silver 1-6, gold 1-6, platinum 1-6, diamond 1-6, onyx, champion (only the top ~200 players in a playlist can be champions)
When it comes to increasing your rank, victory is all that matters. Winning matches will increase your CSR, which is the rating that determines your rank. Losing will cause you to lose CSR. You can drop out of tiers if you’re not careful: lose too many games as a gold, and you can drop back to silver. Technically, a champ could drop all the way back to bronze if they kept losing enough. You will only see your CSR rating if you are Onyx or higher. After every match, you will see how much your rank increases or decreases in the post game report.
If you win a match against a team who’s CSR is much higher than yours, you will gain a lot of CSR; if you lose against a much better team, you will lose CSR but not as much as if they were equal in skill. Alternatively, if you get matched against much weaker opponents, winning won’t boost your CSR that much, but losing would be detrimental. The system tries it’s best to make matches fair.
In ranked playlists, if you quit or otherwise don’t finish a match, you will suffer a CSR drop and get a matchmaking cooldown (aka ban). However, there recently was an update that enacted a “soft forfeit”, where if you leave after someone else on your team has already left, you will not be banned for it (you’ll still lose CSR as if you lost the game, though).
The highest rank you achieve across all playlists is recorded on your Waypoint profile, and remains there even after seasons reset (until you get a new personal best).