For a bill of 15.73, move the decimal over once to the left. You get 1.57. (drop the 3). That's ten percent. Let's say it's 1.50.
Half of that is 75¢. Half of ten percent is five percent so now you have ten percent and five percent. Add them together to get 15%: 1.50 + 0.75 = $2.25 = 15% tip.
20% is even easier. If ten percent is 1.50, twenty percent is double that: $3.00