The 2×2 rule
Beginner technique
How many stars can fit in a 2×2 block?
One at most. Any two tiles in a 2×2 block touch each other, so a block of four tiles can never hold two stars.
This is why small regions are the best place to start. A region that fits inside one 2×2 block could not hold its two stars, so a real region is always bigger, and a region made of just two 2×2 blocks must have exactly one star in each. Cut a region into 2×2 blocks in your head: if it splits into exactly two, you know one star lives in each half.
The same count works on rows. Two neighbouring rows need four stars between them, and they split into 2×2 blocks side by side, each holding at most one.