First of all getting married outdoors is a great option, like Zaku mentioned. Secondly you can cut costs by asking friends to help with things. I was recently in a wedding where I designed the invitations, save the date cards, programs, etc. and that was my wedding present to the couple. It saved them a lot of money because I was able to use a printer I have used before who worked with me to save money on the printing costs (which they did pay for).
I know a lot of bridal shops run sales a couple times a year. A friend of mine (a different wedding) was able to get a huge discount on her dress (half off, I believe) for having all of her bridesmaids/ groomsmen buy their dresses/rent their tuxes form this specific place. And I think they ended up cutting the bridesmaids a 10% discount on their dresses. Also, they could buy the flowers wholesale (from a farmer’s market or somewhere similar) and assemble the bouquets themselves. Or the bridesmaids could assemble their own bouquets and it would be something fun for the bride and her friends to do together.
The only thing I would recommend not cutting the budget for is the photography. A crappy photographer can really ruin wedding memories.
For the music you can always ask someone who is majoring in music at local university to perform. Just put up fliers. As a former broke art student, those freelance fliers were always worth a call. You can pay them less than professionals and they will be happy to get paid (but don’t be a total miser about it either).
For the reception they can create a playlist on their iPod and just let that play. Like miltonandmichele said they can look for someone who is just starting off to help with various things. It gives them experience and allows them to not pay as much as they would to an established professional.
If they get married in the afternoon, then the reception wouldn’t have to be heavy food, but maybe a lighter fare which could really save money.
I hope this helps, especially since I wrote so much. I’ve been in a lot of weddings…