You can clean a plain tutu by washing it in lukewarm water with a small quantity of mild detergent. To avoid crushing, wash it in the bath!
If your tutu is beaded, or if it has a metal hoop, cleaning is more of a headache. The hoop will rust, so it has to be removed before washing. If beads are glued not sewn, they may come off in the wash. Both beads and sequins can bleed color on to the fabric. Unfortunately, dry cleaning isn't a solution, as chemicals will ruin the frill.
This is another good reason for designing your tutu so the embellishments can be removed before washing!
Some dancers simply never wash their tutus. Instead, they spot-clean the areas most affected by sweat, and keep the rest fresh with odor-removing sprays such as Febreze. If you're going to use Febreze, leave the tutu to air after treatment, and make sure it's completely dry before packing it away.
Not washing your tutu will certainly shorten its life because sweat, body oils and make-up will eventually rot the fabric - but in some cases, that's preferable to the risk of losing the whole tutu if it doesn't survive washing!