I've got one of those flip flop hubs, and I need to remove the freewheel side and either service or replace it as it has started slipping really badly. What tools do I need?
You need a freewheel removal tool.
That looks to me like it will take an FR6, but you should measure first if you're planning on buying. Although, this will likely be the only time you ever use it unless you open a bike shop.
Your local bike shop will almost certainly have one of these and be able to whip it off it no time. They might not even charge for such a small job.
Sheldon brown has instructions on the rest the removal. Basically, you just need to put the tool in a vice, place the wheel on it and turn. He recommends using a quick release skewer to secure the tool, but you have solid axles so just be careful.