We have some basic, but effective battery operated lanterns to rent that are best for car camping or short backpacking trips. These are great for what they are, but we want you to know that they will not cast as bright a glow as a propane-fueled big lantern some campers use. Those gas fuel ones are too fragile and impractical for renting. The glow on these is good enough to light up the picnic table at night; make your way to the bathroom after dark; or to curl up and read by.
As a supplement or alternative to these lanterns, also consider a hands-free flashlight style - the LED headlamp. Headlamps are much better than flashlights, but not too conducive to chatting around camp - such lights perched on top of your head shine bright into the eyes of the person you're trying to talk to. Also, a lantern is particularly helpful if you'll be in a fire-restricted area that precludes building a campfire. The headlamps are better for backpacking as they are much lighter.
We test our lights with batteries before we ship to make sure all is working ok, but WE DO NOT INCLUDE BATTERIES WITH ANY OF OUR LIGHTING. Most of the lanterns we rent use AA batteries - you can get the cheapest or most expensive as you want and keep them afterwards for other uses. Some lanterns are rechargeable from a USB port, so be sure to top those off. Cushion the lanterns well when you send them back so they don't shatter enroute.
Lanterns are pretty easy to operate of course, but for some photos on how to use, see more details on the operation of our rental lanterns.