The combination list
The most important aid when solving kakuro puzzles is the combination list. It is invaluable — look things up often in the beginning. With time you remember which digits are possible in a sum, and solving gets much faster.
The combination list shows which digits can make a given sum with a given number of cells. For example, the sum 10 across 3 cells has these possibilities:
10: 1 2 7 10: 1 3 6 10: 1 4 5 10: 2 3 5
So there are four different three-digit combinations giving the sum 10. Now suppose your target sum is 11 across four cells, and you have established that one cell is 1. That leaves 10 across three cells — and since the row cannot repeat the 1, the list above leaves only one possibility: 2, 3 and 5. You do not know where they go, but you know those three cells hold 2, 3 and 5.
The first thing to do is look for sums with only one possible combination. That makes finding the digits much easier.
EM: Single solution
Look at the crossing between two sums. If the crossing cell can hold only one digit, that must be the solution.
Example: a crossing between the sum 23 (3 cells) and the sum 7. The combination list shows that 23 across 3 cells has only one combination: 6, 8 and 9. Since the crossing sum must be 7, the crossing cell must be 6 — 8 and 9 are impossible within a sum of 7.