How do I go about getting my songs pressed on vinyl with out a record label?

It’s easy, just not really cheap.
You’ll need a master, made from a really good quality recording that’s been tweaked and perfected by someone who knows what they’re doing, like a sound engineer. From that recording you can make a master. You can google for places that will master/press vinyl albums for you. I googled and found several in the LA area alone.

You’re looking at roughly $300ish for the master, and if you want a run of 100, will be around 800–900$, so you’d have to sell them all at the very least $9 to break even.

Depends on your area. I used to do that a lot (ie small orders for new bands etc) until CD burners came along. Basically I’d do all the paperwork, artwork, etc, and even physically transport the copies by car, and get paid something like 10%. It was a good deal for the bands that didn’t neet to deal with the hassle, and a fun job for me. Anyway, tell me if you need details, but as sinscriven just said, it’s not that complicated. Are the songs yours?