Here was my under $1000 wedding. Yes, I actually did this. We were planning to pay for it ourselves, but at the end, our parents kind of shrugged and decided to split the bill.
Feel free to steal, adapt, or ignore these ideas.
Venue (both ceremony and party): home. No need to book in advance, pay fees, etc. We did advise guests to bring their own lawn or folding chairs.
Officiant: friend who is reasonably articulate. There's an online church-of-nothing-in-particular that will ordain pretty much anyone for a modest fee.
Photographer: friends and family. (A few of our friends and family are actually pretty talented.) (One of our friends, who has photography hobby, chose this as the thing to shell out for in an otherwise budget wedding that took place in a park. I get it.) If you do hire a photographer, consider if there's any way you can shorten that hour of standing around outside either venue while different combinations of cousins get photographed.
Wedding party: nobody. I hate the idea of sending friends out to get clothes and shoes they're going to dislike and only wear once, plus it's annoying. If you do have a best man, bridesmaids, etc., though, consider not insisting that they all match.
Food: Costco. They have sandwich and cold cuts platters, ready-made things, things you can make with little to no fuss. They have cakes in several flavors, too. Some of the guests got wind that we were trying to do our own cooking and brought stuff we didn't need. We had so much food.
Flowers: Grocery store, and only a few. Not my thing.
Music: Nope. I just didn't feel like it.
Alcohol: Also no. Most of the people I know don't partake. I think a few might have brought a little for themselves, which is not a problem when it's at home.
Guest list: something under 60. Fits in the house better, small enough you can actually talk to people, and they can get to know each other. Also far easier to seat, feed, etc. We did have sort of a second reception later, for some of the family and friends where DH grew up, but that was just a tea party with the good china at his parents' house.
Three things I did really differently than most, and that I wholeheartedly recommend:
1. Casual dress for all. It was a warm day, and nobody minded one bit skipping the formal/party attire in favor of backyard barbecue clothes. People actually relaxed, including us.
2. A "stage manager." This was a college student friend, not so close as to need to be a part of the production, who volunteered to hang around that day and set up, clean up, and generally help make things go. This is who was dispatched at the last minute to go get the ice that nobody thought of sooner. I'd happily pay such a person if I were having another such occasion, but I think they saw it as their gift at a time when they didn't have a lot of financial means. It was a wonderful gift.
3. No religion, minimal ceremony. Obviously, this is a personal choice, but I've endured entire Catholic masses at various times in support of friends, and sorry, but it's miserable. (Think of it this way: if a friend asked you to sit through a whole ceremony for a religion you do not practice or believe, in the cause of supposedly saving your soul, would you see it as a favor to you, or just an obstacle between you and the food?)
The whistle doesn't pull the train, and the wedding doesn't make the marriage. I've never regretted having less wedding.