Do you have to make a reservation before showing up ? Or can I just show up and if there's availability pay?

Definitely reserve online if you want a guaranteed spot!

I have been to Boyd Lake SP numerous times and I have never made a reservation. We have never camped there (I'm pretty sure you should get reservations for that), but we use the beach and put our kayaks in there. It can get crowded, but we usually try to get there early (before lunch).

Yes you have to go online and reserve. This also makes sure you are not wasting your time. Most weekend gets filled quickly