Proxy services - how do they actually work?

Hey guys, I'm looking for a few private proxies to play around with (Social media stuff) and was wondering how the sites offering these services actually work? Is there a physical server which has many individual VPS proxy servers installed? Would it be possible to actually create my own proxy servers (100+) on my VPS?
Sorry for the dumb question, but this is absolutely foreign to me and I really want to understand the process instead of spending money on something I might even be able to configure myself for testing purposes (1-2 private proxies) and maybe later for extended use (100's of proxies).

Different companies work the different way.
It is possible to create N proxy servers on your own VPS, but you need to have N ips for that.

It's pretty easy to set up your own proxies. You just need a VPS with squid proxy server installed, and a host that's willing to allocate more IPs easily.

However, it won't make sense with 1-2 proxies since the VPS is a fixed cost. While additional IPs may be cheap (~$1 per IP address), your provider may also want to sell them in "blocks".

Typically you would want to set up a VPS and get fresh IPs. That way, unlike proxies obtained from a typical proxy/VPN provider, you know the IPs haven't been abused by someone else before.

You would also have flexibility in picking a provider that is geographically close to your billing information, and ideally isn't classified as a "data center" by ISP databases.