I start by making a list of the comps I want to enter. I bottle condition, so I have to make sure to have things ready before the deadline. If the deadline is already published I'll mark the date before that when I want to bottle the beer. Sometimes it's two weeks before, sometimes I might bottle a week before if the comp has a gap of a week or more between dropoff deadline and judging (larger comps like NHC and State Fairs etc).
I calculate backwards what day I need to brew the beer to be ready on bottling day. With my equipment and system I can brew two beers in a 6-8 week period, alternating the weeks. Brew Week 1, Brew Week 2, Transfer Week 3, Transfer Week 4, Bottle Week 5, Bottle Week 6, Week 7 or 8 drop off at comp.
Last year the comps were spaced out just enough that I felt that each previous batch wasn't fresh, so I ended up brewing 7 batches of my CDA recipe to have a fresh one for each competition. You don't have to go to that extreme of course. For things like NHC with a second round, I would just automatically plan on rebrewing it so you have it ready if you advance, and if you don't you have a fresh batch for other comps (and personal consumption!)
I haven't been brewing as much this year or entering as many comps, but last year I had a very detailed schedule set up. That's the only way I could keep track of it.