The core principle here is that food will go bad over time so you've got three main ways to handle that. Cooking at campfires or stoves gives you the best nutrition but won't last too long while smoking your food in smoke houses keeps it fresh for about 5 days, which is pretty decent. If you're planning longer trips, drying is your best friend - find those drying racks and your food will last quite a while even though it won't be as nutritious.

Something interesting about preservation - whenever you're checking your inventory you'll see the freshness shown as a percentage and color, so keep an eye on that especially for meat and other perishables. The Master Cook and Art of Preservation perks can really help stretch out those expiration times if you're into that sort of thing.

Now if you do end up with food poisoning, don't panic because there are a few ways to deal with it. For mild cases just getting some sleep might do the trick but if things are looking rough, you'll want to get your hands on a Digestive Potion. You can buy these from apothecaries, or if you're feeling crafty you can make them yourself with thistle, nettle and charcoal. The smartest approach though is preventing it in the first place - try to smoke or dry most of your food before long journeys and don't hoard stuff that goes bad quickly unless you plan to cook it soon.