So, in terms of actual mechanics, here's how it'll work. There are three areas you can explore: the beach you start at, a cave area, and a forested beach-y area. You get 8 time points during this competition, each of which represents 5 minutes of time.

You can spend Time Points to do the following:

 1 TP to move from one area to another
 1 TP to search a particular section of one map (just move your character token to that area - we aren't using grids for combat or anything) - you'll find a couple Pokemon and can choose to engage with one of them. You can also use Bait as you search.
 1 TP to engage any Pokemon you've previously seen, as long as you haven't changed maps since seeing it in a search (this includes if a Pokemon runs from you)
 1 TP to survey a whole map, which can net you pointers about where to search for certain Pokemon, as well as give you a +3 bonus to the rest of the search rolls you do in that area.