No matter how seldom you use your firepit or how careful you are with its usage, eventually you're going to have to clean the thing. It's a task that no one wants to do, but well, sometimes you just don't have a choice. Don't worry, while that pile of ash and charred wood may look daunting it's actually not that intense a job.
The first thing you need to do is determine what type of firepit you're dealing with. Copper, iron, and slate are all common materials used in portable firepits these days. If you have a sunken firepit, chances are it's stone or slate, which is going to make your job a lot easier. If you're dealing with copper (especially lacquered copper), you're going to need a very gentle cleaning strategy.
First, get rid of the ash and charred debris lining the bottom of the pit. If you can lift your pit, this is a simple matter of overturning it into an ash bucket (NOT a trash can; the possibility of still-burning embers in there is very real, and could ignite household trash). If you can't move your pit, use a small broom to sweep the ashes into the bucket. Wear leather work gloves to protect your hands.
The next step can be done with a rag or thick paper towels. Lightly wet the rag and wipe down the inside of the pit to remove ash clinging to the sides. If your sunken pit has a built-in drain, you can actually hose it down at this step.
To make the pit look nice and new again, apply a light solvent and gently rub the pit in small circles. Don't use harsh cleaners or steel wool, though, as they can damage your pit. Vinegar is a good choice all around. If your pit is copper, buy a copper-only polish to give it that extra shine.
And there you go... In just a few easy steps you've gone from a nasty pile of junk to a lean, clean firepit ready to use!