I've been there 6 times that I can count off the top of my head- 5 times to the south rim and 1 time to the north rim. I've hiked into the canyon twice- 1 day hike and 1 time we backpacked 5 days.
There is limited water available in the canyon but there is some. We planned our nights and mid-day stops to coincide with springs. It is much hotter in the inner canyon than it is on the rim. We went backpacking in early June and the rangers almost would not let us go. We were from Texas so it wasn't a problem for us. We carried heavy packs because we had to carry a lot of food and we carried a lot of water. Otherwise it was not a real difficult trip. We did not carry tents because it wasn't necessary. We actually did not go to the bottom of the canyon with our backpack, we went down the grandview trail, followed the tonto trail west, then came up the bright angel trail.
When I did a day hike in the canyon I went down the kaibab trail to the river, crossed over to Phantom ranch, and then back up the bright angel trail and walked back to my car. That was a long trip for a day. I was in pretty good shape that time and made it to the bottom in just over an hour, but it took maybe 3 hours to get back up. The hermit trail farther west is probably much less crowded. The kaibab trail wasn't crowded but the bright angel trail is very crowded.
IIRC in the vicinity of the visitor center there is a trail that goes a long way each direction following the rim.