On a day hike, you want well-broken in shoes that are appropriate for your trail, some comfortable socks and then your clothing would be matched for the weather, a day pack with a water bottle or hydration system in it. How much water you carry will be dependent on where you are going and the time of the year. The food for your day hike should be something that will appeal to you on the trail. That is the starter. Then maybe a small first aid kit for any blisters you might get from hiking or maybe a pair of tweezers if you are going to hike in the desert. You might run into a cactus. One of the things I always find in the bottom of my day pack even though I am just going for a day hike is a little head lamp. I always carry one for contingency because you never know and it is always good to have light.
