There are various ways of doing Single Transferable Vote. This is the simplest easiest way. A more complicated hand-count is used in Cambridge Massachusetts, but the simple brief one described here is just as good.
Voters rank any number of candidates in order of preference.
N is the number of seats in the election. 1. 1 at a time, each ballot is removed from the ballot box and assigned to its highest-ranked candidate who isn't elected yet. This is much less important a problem than it sounds. The important thing is that we elected our 1st choice, and everyone has a better chance to help their 2nd choice than either of us would have had in the current non-PR system. If the ballots are stacked, then flip a coin to determine whether or not to turn the stack over before beginning to draw from it.