There are several hiking options in Uluru but the most interesting, and also the longest, is the 10km path around the rock, well-maintained with signs marking the holy places where photography is forbidden. You can see all sorts of interesting things along the way: paintings, holes, caves, furrows that look like they were made by human hands, sacred places, and more.
There are two possible options when you reach the magical Uluru. You can climb to the top, but doing so is not well received by the indigenous peoples, who consider it an act of sacrilege. Alternatively, you can go for a long walk along the Mala Walk, a route which stretches for a few kilometres. You can go quickly in an hour, but you may want to stop and take photographs. Also, along the way, there are many places where you can appreciate the art of the Anangu Aboriginal rock. The Mala Walk ends before Kantju Throat, a deep crack on Uluru. The whole area is considered sacred to the Aborigines, so it is essential to show respect. Don't miss the magic of sunset over Uluru, when the sacred mountain literally changes colour, like a fluorescent bulb. Entrance to the park costs 25 Australian dollars and provides access to the site for 3 days. Possibly the best time to visit is during the austral winter, very cold at night, but pleasant during the day.