Summarize this article:

Scroll through your world until you find the Sim you want to delete from FreePlay. If you're controlling the Sim in question, doing so will open the Sim's options pop-up menu. If you aren't controlling the Sim, tap the green "Switch Selection" icon in the upper-right side of the menu to switch to the selected Sim, then tap the Sim again. It's a red and white circle with a slash through it. You'll find this option to the right of the Sim's face at the top of the pop-up menu. This green button is at the bottom of the pop-up window. Doing so immediately deletes the Sim from your FreePlay game. This decision cannot be undone.

Summary:
Find a Sim to delete. Tap the Sim you want to delete. Tap the "Delete" icon. Tap YES when prompted.