Riot, how does ranked placement work?

Hey riot, I know there are already a lot of posts on various boards about people complaining about unfair placements, so hopefully this doesn't seem like another one of those. Honestly my ranks and record doesn't really matter, I just want to know how placement matches determine your rank, especially after you were ranked in the last season? I know there was a soft reset but what exactly does that mean? And how much of your new rank is based off your placements and how much is based off of your previous rank? Hopefully an answer to these questions will explain everyone the reasoning their ranked placement and make them a little bit less upset about their new rank.