How do teams schedule their games against eachother and when did that system start???

The conferences determine the schedules. However, individual teams schedule their own out-of-conference games long before the season starts. I have no idea when this 'system' started as football is over 100 years old.

Non-conference games are mutually agreed upon by each team. With traditional non-conference rivals (a la Clemson-South Carolina or Notre Shame-USC) it's pretty much already set when the games will be played.

Conference schedules are determined by the individual conferences.

It's been that way since college football started.

The conference games are set by the conference officials. The non-conference games are negotiated and scheduled by the individual schools. They can play whomever they want that they can get a game with during the weeks they have available. Often, the two schools will negotiate things like home or away, how the ticket sales and concessions will be divided, etc.

Schools that were close together started playing each other and forming leagues or associations. Eventually there began to be rules governing school sizes so that all the games wouldn't be so one sided. This is pretty much how it's done now, except for non league (or conference) games. Those are usually determined 4 or 5 years in advance by the athletic directors.

They schedule who is in their conference. They rotate every year playing away or at home against each conference teams. Every team schedules their non conference games by just negotiating if they want to play them or not. If teams need to get a game in then they look for teams with the same open date as them. Most of the good teams schedule good non conference teams so they have a good strength of schedule and good competition.

The conferences establish the confernce schedule. The schools sign contracts for out of conference games at least two or more years in advance to account for scheduling conflicts and etc. It's been around for a very long time.