How to marinate cheese
A lot of cheeses are naturally brined (feta, for example), and marinating cheese is not much different.  For the best effect:


Pick a porous cheese
Cut off the edges if the cheese has a skin
Cut into smaller pieces to increase the penetration
Press it dry with towels (or paper towels) 
You can inject the cheese to get more flavour in it
Marinate in flavours that compliment the cheese
Let the cheese soak for at least 4 hours (more for less porous cheeses)


If the cheese is really wet (like feta), add weights to the drying process (like a pot or heavy plate), and let it drain until the surface feels dry.

Note that many cheeses are already salty, so balance your marinade with this in mind.