Dye Sub, as said above, is the standard for event printing.
You can buy standalone printers (to be used onsite connected to a laptop) or all in one systems which include a kiosk like screen (so your customers can browse their shots and pick the best ones to print). You can also hire 'event systems' from many professional camera and lighting companies and maybe even see a demo in-store.
Costs on Dye Sub printing isn't too high either. You buy a roll which has the width of a standard photographic size (such as a 6" wide roll) and the printer will automatically trim each print to avoid wastage.
Whichever printer/setup you decide to go for, it is wise to consider taking an assistant with you to take orders, payments, select photos to print, slip prints into a folder...etc... If there is a delay between the shoot and the viewing, this can result in a lost sale (though this does depend on the type of event you are covering). Also remember that not everyone will be carrying cash, so have a think about how you can take alternative payment for your prints.
Chris.
