I'm sure everyone knows already, but I thought I'd mention not everything has to go in the fridge. I keep potatoes, onions and garlic, squashes, rutabagas in a dark cool cupboard in my kitchen. There are probably others; these will generally last a couple weeks in there. If I buy a big rutabaga (swede) and only use half, I'll keep the remaining half still in the cupboard till I need it.
Tomatoes live on my countertop, along with most fruit, though not berries. If I pick too much chard at once, I'll put a big bunch in a jar of water, like a bouquet. Cabbage, kale, and other leafy greens are fine like this too, even as separate leaves. I leave in on my countertop out of direct sunlight and it'll last a few days; in fact, cabbage ends up even more crisp than when I put it in (even if I picked it from my garden). It might work with lettuce too--worth trying.
What I personally keep in the fridge: carrots, cucumber, peppers, mushrooms, grapes, berries. The small things (like berries) go in a container, but everything else goes in a drawer or on the shelf.