I can tell you what does NOT affect your placements: your KDA or any kind of personal performance indicator. All that matters is whether you won or lost the matches.
No one knows exactly how it works because Riot hasn't made it public. It does take into account your ranking in the previous season, your opponents' MMR (in each match), your teams' MMR (in each match), and how many games you won. Can't tell you what has the most weight though.
If you are placed in a rank you don't deserve, you will rise! It's not your final rank. Placements don't matter THAT much.
-- Person who was Gold 1 in season 4 and got placed Silver 4 in season 5... then ended in Platinum 5.