Believable costuming can be achieved on a very tight budget if you plan ahead.
There will always be some performers who will want to keep their costumes (especially kids and their parents). If you are prepared for this ahead of time, it can work to your advantage. Send home a letter asking if they would like to keep the costume, and if so, would they consider making a small donation to help cover costs? (No self-respecting person is going to ask to keep the costume yet refuse to give a donation!) I was able to outfit an entire show this way without using any of our bake sale money.
If you are doing a highschool production or have a connection with a highschool, you may be able to find a few students who are interested in careers related to costuming such as fashion design or seamstressing. They would probably be glad to get some extra experience. Or, you might even have a home economics or sewing class that could take on the productions costuming as a class project.
Form a partnership with a local community theatre. They quite often have a costume vault that they would be willing to have you borrow from.
A local fabric store may be willing to give you a discount if you put a small thank you ad in your program.
Don't throw anything out! Save all your old costumes. Most stuff can be reused, provided you store it in an organized manner so everything stays in decent condition.
Send out newsletters a few months in advance to ask for old halloween costumes and spare fabric. People will be happy to unload some of their junk, and you'll have tons of costume stuff. Anything that is unwanted can always been given to the local charity shop.
Recycle items that don't seem like costumes, but could easily be transformed -- old curtains are a great source of material (think Sound of Music!). I actually have sewn dresses out of old curtains.
Don't do more work than you have to. Most of the time, making alterations is easier than making things from scratch. If you start enough ahead of time, most shows can be costumed just by scouring the local second hand stores. If you ask nicely, some of them may even be willing to keep an eye out for certain items for you.
It is very easy to get caught up in the "look" of the show. Remember that ultimately what counts is that we are enjoying ourselves, and putting on a good show. Quality of performance should always be your first priority, not what the performers are wearing.