First, overlap the big numbers: 8, 7, 9, and 6.
Next, cross out squares that you know can be crossed out, starting with the rows. You can put Xs around the single black square in the "1,1" row, because it cannot be any bigger than one square. You can also cross out squares in the "4" row below that, because the black squares can never reach the right side. You know that the two squares in the "3,1" row must be part of the 3, so you can cross out the two empty squares to the left where the 3 will never reach. Finally, you can cross out squares in the "5" row, where the 5 will never reach. So far, the grid should look like this:
Now cross out squares in the columns. You can cross out one square at the top of the "6" column; no squares can fit in that area. You can also cross out the top squares of the two columns of "5", where the 5s will not reach. In the last three columns, you can cross out squares at the bottom and top.