What tools/steps should I take in order to fix this backyard fire pit up. Also, how could I make its surroundings look better as well.

If you go to a big box store like Home Depot or Lowe's, they have fire pits and stuff for sale. They have an idea book that you can look through.
Do what I did. I pretended to be interested and brought several images of my yard. They gave me loads of ideas! But they wanted to get more involved, add on so much stuff that it was becoming expensive. But I got several ideas and ended up doing it in stages according to what I wanted.
If it would have been cheap enough, I might have had them do it.

But honestly it is hard for us to know what you would like.

Zs123, I would simply use bricks all around it, and fire pit grates in the center and that's it. If you want to see and understand what are the best trends in nowadays fire pits grates, you can simply visit here ( link: https://mygardenzone.com/best-... ), it's an article with a dozen fire pit grates of any type.

It's such a mess at this point; I'd just start over. The weeds are numerous and obviously the weed fabric isn't doing you much at this point. Also there's no boundary to keep the gravel in place so it just flings everywhere.

Clear it all out and make a plan.

Here's just an idea. Visit a metal recycler or several. What you're looking for are the ends cut off of big propane tanks. I have found sizes from two feet diameter to five feet. The larger the tank end, the shallower. They cut them off so that they can split the main part of the tank and break it down. The big ends are up to 1/2" in thick. They are easy to drill, so it's not hard to make drain holes in the bottom. (The make outstanding planters, too.)

They can be partly buried, set on the ground, or set on a short section of big iron pipe. Or have legs welded on.

Probably the cheapest ground treatment is irregular gravel or crushed stone. Or 12" concrete pavers. If you set the pavers on sand, you can come in at the end and pour dry concrete ready mix over it and between the pavers, keep it wet for a day, and it will set up and keep the gaps filled.