To get a hit location without needing another roll, look at the least significant digit of the damage rolled and whether the to-hit roll was even or odd. E.g. damage 3 would be the upper right arm if the attack roll was even, upper left arm if odd; damage 12 would be right foot if even, left foot if odd. The numbers are arranged so the heavier damage tends to be the result of hits in more vulnerable spots, while still allowing the full range of ordinary weapon damages (1d4 to 1d12) to fall almost anywhere on the body. One trick to using this fluidly is to interpret the results of smaller die sizes as covering larger areas, so a 3 on a d4 might be anywhere on the arm or even mid-torso, while a 3 on a d12 is specifically the upper arm.
As I use it this is purely informational to help describe the result, though I might make an ad hoc ruling if it seems particularly relevant, such as requiring a saving throw to keep holding on if they’re clinging to a rope when they get hit in the arm.
(This is a re-post of the chart that originally appeared in the post on Death & Dismemberment for 5e, since I think there are folks who skipped it since they’re not interested in D&d 5e content).