Ok, I will give it a try.
A number at the top of a column indicates the total of the numbers in the spaces below.
And a number at the left end of a row indicates the total of the numbers in the spaces to the right.
The numbers that make up the total will be in the range 1 to 9 and will not have any repeats, so the best way to start is to find totals that can only be made up from one set of numbers. For example, if the total is 4 and there are 2 spaces then the spaces must contain 1 + 3 because 2 + 2 is not allowed. Other examples are:
3 squares totalling 7 = 1 + 2 + 4
4 squares totalling 29 = 9 + 8 + 7 + 5
Of course, you can't tell immediately which order to put them in, so look for intersecting sums. For example, if you have a row of 3 spaces adding to 7 you know it must contain 1 + 2 + 4. If it intersects with a column of 2 spaces adding to 12 then the column must contain 8 + 4 because it can't be 10 + 2 or 11 + 1.
Have fun!