Frozen is always a great option. Not only is it convenient (no expensive veggies to throw away because they rotted before they were used), and cheap, but it's also just as nutritious.
Check your local grocery stores to see what's cheapest where. We make a weekly drive out to Wal*Mart because I can get organic milk, cheese, eggs, FF 1/2 and 1/2, and cilantro for very cheap. Our Wegman's sells cilantro for $1.99/bunch. Wal*Mart sells it for 68 cents. Definite savings, since we use it every week.
Buy at local farmer's markets! It's usually cheaper...and sometimes dramatically so. I can get a bunch of leeks (skinny, anemic things) at Wegman's for nearly $3.50 (or more), while two HUGE (we're talking 2.5-3 feet long and 2-3" in circumferance) leeks are $1.50 at our farmer's market.
Amazing! Of course, it's easier to find farmer's markets throughout the winter if you live in a warmer climate, but some areas have a farmer's market inside in the winter, so check your area!
Plan your meals so you use all of a veggie, especially big ones. For instance, if you buy a cauliflower, you're unlikely to use the whole thing for one recipe--so only buy it if you have planned recipes enough to use it all that week.
Buy in bulk, if you'll use it all before it goes bad. I can get some fabulous deals at Sam's Club (i.e. Costco) for green beans, spring mix, bell peppers, etc. However, you end up with a huge amount of food. Either freeze the leftovers, if you can, or make sure you can use it all before you buy it.
Buy vegetables in season. Even though it's getting pretty cold in some parts of the U.S., some vegetables are in season. Look for chards, cabbages, broccoli, and brussel sprouts. They do well in cold weather and may be available for less cost locally. Our green beans go down in price from about 2.99/lb in the winter to about 99cents/lb in the summer because they're in season.
Hope this helps!