Firstly, please forgive me if I get some terms wrong. I'm learning this as I go.

Recently, we had a clogged drain at our house. We purchased some drain cleaner, and overnight it seemed to work.
The next day, it started to clog again, and after a vigorous plunging, the drain cleared up.
This was a few days ago, and yesterday my neighbor comes to tell me that there seems to be a large puddle next to our house.
I looked in our crawlspace and saw that there was some standing water in there. I crawled around inside, and saw no leaks. I asked my wife to flush the toilet for me, and then saw that there seemed to be a major leak in the main sewer line.
This line is black plastic, and I'm assuming it is ABS. It comes down from the house, makes a 90 degree turn, and goes out from there.
At the 90 degree joint to the line into the house, is where the leak is.
I'm not sure how to go about fixing this.
I've done some regular plumbing before new sink, toilet replacement, that sort of thing, but I'm not sure if I should get a professional to do this.
Any advice/suggestions would be greatly appreciated.

Is the main sewer line hanging from joist in crawl space or goes underground and out? Exactly what is visible?

Good questions. Does it appear to leak right at the elbow joint where the elbow and pipe were glued/welded?

The main sewer line comes down past the joist, then has a 90 degree bend before going through the foundation. I can see the bend and the piping into the wall. The leak is at the 90 degree bend, at the top of the bend where it connects from the pipe coming down.

This sounds like a failed glued/weld joint which can't be patched by throwing on more glue. It also sounds like there may be some partial blockage since this drain should never build up any pressure which would force this much water out the top of a joint. I would cut out the elbow and several inches of line on each side of it and then glue/weld in a new elbow using hubless collars