Are you looking for a circuit that lets you flash or drive an LED from a single battery? This article from EDN has just what you’re looking for:
Simplified white-LED flasher operates from one cell.

Here’s some of the highlights of this clever design:

• uses a low-voltage logic gate to allow one-cell operation
• uses an inductor whose value is not critical
• operating voltage ranges from 0.8V to 3.6V, so even somewhat spent batteries can run it
• can be converted to non-flasher by omitting components
• low parts count includes stuff you probably already have in the “junk drawer”

If you are looking for a one-cell LED driver, this circuit has a lot going for it. Back in the day, the LM3909 used to be a popular, simple solution, but it’s discontinued (although you can scrounge old stock occasionally)