Here are a few combinations that could start you off:
Salty with Sweet
Salty flavoured cheeses such blue cheese goes well with the sweet tendencies of dessert wines and vice versa. Stilton compliments Port especially well.
Rich and Creamy with Sparkling
The pairing of rich and creamy textured cheeses with champagne or sparkling wines is definitely a combination that should be tried. Would go down well at a reasonably decedent party. A cheese such as Brie or Gruyere would be a good start.
Local Pairings
Another easy place to start when pairing cheese with wine is to try pair up a wine and cheese produced in the same region or state. It won’t always work but is a good starting place and worth a try.