Casting your vote doesn't change...
Most past the post keeps the same format for holding elections - you cast a single vote for a candidate in your constituency.
The difference is that your vote counts for the candidate (or that candidate's party), no matter where you live.
Your vote has the same weight as everyone else’s, even when the candidate you vote for doesn’t end up winning the seat.
There is no longer any reason to vote tactically. There is also no disincentive to vote, even in safe seats.