Every empty cell needs a number. Add or multiply the numbers across a row — using the symbol in the corner — and they should hit the target to the right. Do the same down each column to hit the target below it.
Tap a cell to open the number pad. As you fill things in, some cells will fill themselves in — once only one cell in a row or column is left empty, its value is already decided by the target, so the puzzle fills it in for you.
Feel free to try things and see what happens — nothing you type is ever wrong until the whole grid is complete. If one of the automatically-filled cells turns out to be impossible, you'll get a quick heads-up so you can back up and try something else.
If the puzzle has a rule — shown in the colored pill above the grid — keep an eye on it as you go; it'll change color if something you've entered doesn't fit.
Strategy
Start with whichever row or column has the smallest target — there are fewer ways to make a small number, so it narrows things down fastest.
Once you've placed a couple of numbers, look for any row or column that's one cell away from full — that last cell is never really a guess, it's just addition or multiplication in reverse.
Some puzzlers like to work the whole thing out on paper first, then type in the finished answer all at once — the puzzle will confirm you got it right either way.