Simple Rule: If your guests offer to bring something, a couple of easy and reasonable options are pies, ice, spirits or other beverages, and snack trays for keeping people happy before the meal (full tip on snacks coming soon).
If you’re asking them (or they offer) to bring a side dish (such as green beans, potatoes, salad) consider that if you’re feeding more than about eight people, you might want to supplement with your own, or ask two guests to bring that dish.
Keeping guest foods hot can be a challenge. If your guests can bring their dish in a slow cooker, keep a place open by an outlet for them. Other methods of keeping food hot include chaffing dishes heated with canned heat such as Sterno, or hot plates that plug into the wall. These are a great investment (not too pricey and easy to store).
One other consideration regarding guest contributions: Either have plenty of serving dishes and utensils available for serving guest dishes, or ask that they bring everything needed to serve their dish from the table. For instance, if they bring something in a slow cooker, they’ll need a dish to transfer it to for serving. No matter what, something unplanned will happen with a guest’s contribution so be flexible and go with the flow.
One other note: You’re the host, so nobody should be expected to bring anything. If they ask what they can bring, give them an assignment that feeds 6-8 people (that’s about how many slices are in a pie, for instance). If they offer something specific, just say yes (unless it is something truly unwelcome). Your guests are guests first. If you can’t swing providing everything, maybe a smaller crowd or a co-host are good options.
Resources for further learning: