Start with the smallest meadows
A meadow of one cell has its firefly already. A meadow of two or three cells in a line has only a few choices, and often one of them is impossible because it would leave a neighboring meadow with nowhere to go. Small meadows are almost always the way in.
Look also for meadows that sit entirely inside one row or one column. That meadow’s firefly must be in that line, so every other cell of the line is empty.
“Small meadows have nowhere to hide. Start there.”
Halley
Mark the cells you rule out
Every time you place a firefly, mark the cells it rules out: the rest of its row, the rest of its column, the rest of its meadow and the eight cells around it. Marking these empty cells is most of the work in a Star Battle. The firefly placements follow from what is left.
Any two-by-two block of cells can hold at most one firefly, because any two cells in it touch. Use it to rule out cells near a crowded corner.
Count rows against meadows
When several meadows fit entirely inside the same few rows, they use up those rows. If two meadows lie completely within rows 3 and 4, those two meadows take the two fireflies for rows 3 and 4, and every other cell in those rows is empty. The same count works for three meadows inside three rows, and for columns.
This counting step is what separates the easy days from the hard ones. When the board stalls, look for a group of meadows squeezed into the same lines.
Test a cell by its consequences
If a cell would leave a meadow, row or column with no possible firefly once you place it, that cell must be empty. Checking this for the few remaining candidates in a small meadow usually breaks the last knot without any guessing.