If you're serious about actually going about the process yourself, maybe check out the Explorers Guide: Qatar (the book with the purple cover). You can get it in Carrefour, I know for sure. It's 75 riyals. I think the process is outlined in there.

However, I'm telling you. While I'm pretty independently-spirited and like to do things myself, I'm definitely glad that HR jumped through the hoops for me, or helped me jump through. It would have been a bit daunting without having a driver who knows people at all the places and knew just where to take us and how to fast-track the process.

Let your sponsor take care of it for you, unless you're already finding that your sponsor is a bit dodgy.