First techniques for solving Star Battle puzzles
Start with the smallest regions. A region that is only one cell wide, or a thin strip along one row, tells you a lot about where its stars can go, because they are forced into a small set of cells.
Look for regions that sit entirely inside one row or one column. If a region lives wholly in a single row, that row's stars are used up by the region, so every other cell in that row can be crossed out.
Count groups of regions against groups of rows. If two regions are entirely contained in the same two rows, those regions use all the stars those rows can hold, so any other region's cells in those rows are empty.
Remember the no-touching rule when you place a star: cross out all eight neighbours straight away. Most early progress comes from the dots, not the stars.
When you are stuck, pick the row or column with the fewest open cells and ask which placements would leave a neighbouring region with no legal cell. That contradiction is the next deduction.
More guides on the StarGrid page.