Note that the title of this instructable is "host a cheese tasting party," not "set up a cheese tasting potluck" or "con your friends into bringing food for a party you can't afford to throw." Cheese tends to be pricier than pizza and popcorn; keep your guest list manageable. Too many guests would also distract from the cheese tasting. If you'd prefer to have a bunch of people over for a kegger and provide a cheese tray, do that instead.
Hosting a party
means providing everything, not asking people to bring items. If a friend volunteers to bring something without you hinting around, it's perfectly acceptable to say "yes," but it's also acceptable to turn down a food item at an event you host. If a guest shows up at the door with a food or drink item, you can either serve it or keep it for personal use later. You're not obligated to serve it to your guests.
You'll have to decide what number of guests works best for you, but think about your seating and what you can provide. Six to twelve is said to be a good number of guests for a tasting party.
How much cheese should you get? That depends on when you have your party and what else you'll be serving. Parties during the lunch or dinner hour should serve more food in general; if cheese is the main focus of a party held at 6 or 7 pm, you might want to count on up to 6 ounces total per guest; if various cheeses are just one option at a cocktail party, you might need as little as one ounce for each guest. Bear in mind that the 6 ounces per guest includes ALL the cheese at the tasting; your guests aren't likely to eat 6 ounces of each of the varieties you serve.
Think about your guests; if you know them well, you might have some insight on which cheese types to avoid. When I was buying cheese for this very casual family cheese tasting party, I kept in mind that none of the guests like blue or excessively stinky cheese. There's nothing wrong with choosing mild or common cheeses for a cheese tasting party if you know that they're what your guests would enjoy.
If you need help selecting cheese, try to find a decent fromagier at a cheese shop. If you know what you want, you could just as easily buy your cheese at the local chain grocery store.