There are thousands of wines and cheeses to choose from. How on earth does one know how to pair them well?
For nearly all cheeses, you want four characteristics in your wine:
Good acid (cleanses and activates the palate)
Good fruit (balances the savory, earthy notes of cheese)
Lower tannins (they compete with and can overpower most cheeses)
Extra bonus: bubbles! (they cleanse the palate and heighten all cheese flavors)
Here is a super-quick "cheat sheet" for you. Obviously, there are exceptions to every rule, but this should get you through in a pinch.
Fresh -- Light White wines (Sauvignon Blanc, Pinot Grigio) or Rosé (honestly, Rosé pairs will with almost any cheese)
Soft-Ripened -- Bubbly wines (Champagne, Cava, Prosecco)
Semi-Firm -- Lush whites (Chardonnay, Chenin Blanc) or Lighter reds (Pinot Noir, Grenache)
Firm -- Medium Reds (Malbec, Tempranillo)
Blue -- Bold, Fruity Reds (Zinfandel, Syrah) or Fortified/Dessert Wines (Port, Sauternes)
Washed-Rind -- Slightly Sweet Whites (Riesling, Gewürztraminer)
And if all else fails:
Match intensity so neither your cheese nor your wine dominate
Go for regionality, as most cheeses and wines "grow up together" and will pair nicely