I'd like to point out that even when No1Servers couldn't bare with the DDoS attacks they were receiving they we're doing very well by refunding people for their gameservers. No1Servers was not a scam company at all..
On the topic itself:
When someone is hosting a server for you (ex. a company) they are giving you access to the server files of yours and they give you an account to a game control panel or something similar that alloows you to start/stop, update and up-/downgrade your server, depending on the company ofcourse as everyone of them have their own panel.
The amount you have to pay depends alot on the player amount you want to have on your server. Most of the companies are usually selling slots for around 0.10-0.20€
A few options for companies hosting your server:
www.og-servers.net (Don't have personal experience)
www.serverffs.com (Very good pings and low prices, but no support and very low CPU usage limit)
www.busign.nl (Good customer service with low prices, hosted on very strong machines, but I'm not sure if they offer game hosting atm)