How exactly does one buy IP addresses? Do you have to run your own BGP instance and peer with others? Could I, for personal use by a /22 and control my own network? How much does that cost to do?
Next you need to either get a direct allocation from a RIR (RIPE, ARIN, APNIC, etc) or buy/transfer IP's from another party. Depending on the IP's history, it may or may not be subject to transfer regulations (showing a need for it).
Once you've got an AS and IP's, you can advertise them out multiple ISP's with BGP. If you've only got a single provider, you can have them announce it for you and statically route it to your side of the interface.