Most people use one of three options for carry water or sports drinks. They use handheld water bottles, hydration packs that are affixed to the back, or complicated fanny packs that carry water bottles. Each one has pros and cons.
Handhelds: Handhelds have three major advantages: Having your drink in your hand helps you remember to drink regularly, they offer some hand protection should you fall, and they are easy to fill at aid stations. The downside to handhelds is weight. It can be difficult to carry a 20-24 ounce water bottle all day. Also, I've had some problems with the strap on the water bottle chafing my knuckles.
Hydration packs: Hydration backs hold far more of your favorite beverage than handhelds, and the weight is equally distributed on your back. The backpacks can bounce around if your running form is too “bouncy” (see the section on good form). Hydration packs are also a pain in the ass to fill at aid stations, though you have to fill them less often.
Fanny packs: In my opinion, these are the worst of both worlds. The water bottles are held around your butt, which requires reaching back to grab. Since the bottles are out of sight, there's no reminder to drink. Finally, the pack itself may cause chafing due to bouncing.
It is possible to run without anything and just rely on the aid stations. I wouldn't advise this as a new ultrarunner, especially if it is hot or the aid stations are farther than five miles apart.