Integrating WP into main website

Hey all, I’m relatively new to WP, I’ve tinkered with it in the past but nothing too in-depth.
Anyway, I have a website that I’m working on, and I’d like to have a blog on the front page, as well as several different blogs nestled into their own corner of the site.
I have absolutely no idea how to do this. As far as I know, WP is it’s own site, basically speaking.
I don’t know if there’s a way to integrate WP into an existing site, or if I’m going to have to try another blog program, or what.

The website I’m working on is here

I hope I explained everything alright, if anyone can help I’d appreciate it!

Thanks in advance,
Jay