Answer:
Say that you have a bill for x dollars. then a 20% tip is .2x
.2x is the same as 2 * (.1x)
If you recall, however, dividing by 10 simply involves moving the decimal place one position to the left (if you owe $31.74 for a bill, 10% is 3.17, then multiply by 2 to get $6.34 as approximately 20%), then double it.
This will get you the correct approximation of the tip up to about a cent, and it tends to be relatively easy to divide by 10 (move a decimal) and to double something in your head. Then you just add that onto the bill.