How do you adjust timing with a distributor cap that has latches holding it stationary?

The timing for this type of distributor is set by rotating the entire distributor, not just the cap. The distributor should have a lock down bolt holding it down where it sets in a housing. With the engine NOT running, mark the original position of the distributor with a marker or some white paint. Then you loosten the hold down bolt a little, then see if you can turn the entire distribuor very slowly just a little bit. If it turns a little, then you can hook up your timing light paying attention to the cautions and warnings in the instructions for the timing light or the auto manual being used to set the timing. You start the engine, and slowly turn the entire distributor left or right until the desired timing is reached. Turn off the engine, then tighten the distributor back down.

That's pretty much it in a nutshell!