Place a mine into some of the empty cells so that each number represents the total count of mines in neighbouring cells, including diagonally adjacent cells.
Very simple rules. The logic can be tougher. I'm more than willing for others to add their own tips, my list is not exhaustive. Let's walk through this puzzle.
The first things I look for are: zeroes (no mines anywhere around them), high numbers (8 is particularly easy, but others can also give a lot away), numbers on the edge (as they have fewer possibilities) and numbers physically close to each other but different in size.
The four at the bottom edge qualifies as high, given the edge placement.
There must be four mines in the yellow cells and there are only four blank cells, so they must all contain mines.
The next step involves a few parts. The three at the bottom means that one of the yellow cells must contain a mine. The four on the right edge means that there is only one empty cell around it, including and especially the blue cells, so the blue cells must contain at least one mine. This means that we have found the two mines for the 2 on the right edge, and there must only be one mine in the blue cells, and the white cells around the 4 on the right edge must have mines in.
It's not obvious which of the previous yellow and blue cells contain mines yet, but the big breakthrough here is that the central 3 clue is now satisfied, so all other cells around it must be blank, as marked above.
Now that these blank cells are marked, the 4 on the side and the 3 on the bottom can only be completed in the way above.
The 2 on the left similarly only has one way of being completed, and then the 1 clue at the top is satisfied, so the remaining cell must be empty.
