The best way to start is often to mark where there can’t be any trees, because they would make it impossible to place a tree in another colored shape. (Remember, trees can’t touch, even diagonally). So these two dashes have been placed because a tree in those locations would make it impossible to have one in the blue or red shapes.

Now, looking at the puzzle, we can see that the tree in the green shape must be in the third row. Because there is only one tree per row, we can mark out the two magenta squares in that row.

The blue and the orange shapes are both in only the first two rows. Since there is only one tree per row, the two trees in the first and second rows must be in the orange and blue shapes, and not the magenta.

By this same logic, the trees in the first three columns must be in the blue, green and red shapes, so we can mark out the orange.

This now means that the tree in the orange area must be in the first row, so we can mark out the two blues in the first row, leaving only one blue space – this must be the tree.

There is only one tree per row or column, and there are no trees adjacent to other trees, so we can now mark out a number of squares.

We can now place two more trees – one in the only green square left, and one in the only square left in column 2, then mark all the places those trees have eliminated.

There is now only one place the magenta tree can go. Once we place that and mark off the places that it eliminates, there is just one orange space left to put the last tree.