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What you need
One wrapped gift per player, inside the agreed price cap
Numbered slips of paper in a hat or bowl
About 30 to 60 minutes
The rules
Set the price cap. Agree one spending limit for everyone, such as $10, $20 or $25, and set a date and time for the swap.
Wrap and pool the gifts. Each player brings one wrapped gift with no name on it and adds it to a shared pile.
Draw numbers. Everyone draws a number from a hat. That number is your turn order.
Player one opens. Player one picks any wrapped gift from the pile and opens it so everyone can see.
Open or steal. On each later turn you either open a new wrapped gift or steal an opened gift from someone else.
Replace a stolen gift. Anyone whose gift is stolen picks again right away: open a new gift or steal a different one. They may not steal straight back the gift just taken from them.
Freeze a gift. A gift is frozen after its third steal and stays with whoever holds it.
Final turn. When every gift is open, player one gets one last chance to swap with any unfrozen gift. Then the game ends.
Variations
Yankee swap: Another name for the same game, common in New England. Some groups let each gift be stolen only once per turn.
Dirty Santa: The same game with a looser steal rule. Some groups allow unlimited steals per gift, so set a time limit.
Dice version: Pass gifts left, right or across based on dice rolls while a timer runs. Whatever you hold when it stops is yours.
Theme swap: Everyone brings a gift that fits one theme, such as mugs, snacks, or desk toys.
Office friendly rules: Keep a $20 to $25 cap, ban gag gifts that could embarrass anyone, and cap steals at two per gift so the game fits a lunch hour.
Quick tips
Announce the steal limit before the first gift opens.