A detailed map and compass are first as GPS systems may not work inside the Canyon. Next come sturdy, well-fitting, broken-in hiking boots with traction soles. A backpack, not too large, with which you are familiar, is your portable home. Many summer hikers take no tent, but all need a sleeping bag, sleeping pad, ground cloth and bivvy sack or tarp.
You may not build a fire in the backcountry. Take a lightweight stove, adequate fuel and waterproof matches. One good pan, utensils, a cup, a plate or bowl, an all-purpose knife and toolset complete your kitchen equipment. Choose food with space, weight and a larger than normal appetite in mind.
For sanitary purposes, pack a trowel, biodegradable toilet paper, non-residue soap, paper towels and a small towel. Don't forget a few Ziploc bags to carry used toilet paper and camp trash.
Sturdy water containers that add little more weight than the water they carry, yet will not rupture, are critically important. Nalgene bottles and flexible bladders with or without a drinking tube are the most common. Add a good water filter or chemicals to purify the water you collect, and possibly a pre-filter or folding bucket to deal with sediment. Some hikers use a SteriPEN and pre-filter combination. Some also carry, as backup, a filtering straw.
The layered approach is best for clothing. Tuck in rain gear and a head lamp or flashlight. Bug netting or repellent help with seasonal insect hatches. Don't forget spare batteries for everything that needs them. Trekking poles make both downward and uphill trails easier, especially when carrying a heavy pack.
Duct tape is handy for a myriad of repairs. Keep food safe in rodent-proof food storage containers, like the reasonably lightweight bag, Ratsack. Thirty feet of nylon cord aids tarp pitching, pack hanging and boulder scrambles. Your medical kit should contain blister, cut and scrape, splinter, sprain and analgesic supplies. Also, consider renting a satellite phone, in case of flood, injury or illness.
A good summer hat provides shade to head and face. Sunblock clothing, which is a specialized item, is desirable. Take and use an excellent sunblock lotion, at least SPF 30, even though some studies suggest lotions may not protect from skin cancer.
Take more clothing, including gloves and headgear, and add an ice axe to negotiate slick boulders. Carry a four-season tent.