Calculate 10% by moving the decimal point over one space toward your left. (If you're leaving a 10% tip you've got the answer, although most people don't leave that little).
Now that you have 10% in your mind (or on a napkin), divide it by 2 to get 5%. Add the number you have for 10% to the number you have for 5% together - and you've got 15%.
For 20%, figure out the 10% and multiply by it by 2 (or else add two 10%'s together) to get 20%.