Counting Regions Against Lines
If three regions fit entirely inside three columns, those columns give all their stars to those three regions, and every other cell of the three columns is empty. On a 7x7 grid, looking for such groups is often what opens a Medium grid.
Marking as You Go
Use two marks: a small dot for a cell that cannot hold a star, and a star for a certain one. Mark the eight neighbors of every new star right away; on a 7x7 grid, forgetting one neighbor is the usual source of errors.
After the 6x6 Grids
The 7x7 grids suit solvers who finish the 6x6 grids easily. Start at Easy to get used to seven regions, then move up.