Here's a procedure that works for me. Unfortunately, my vehicle usage almost always requires a full lube job at each oil change so I've only been able to enjoy doing this twice.
This won't work if the oil filter is on too tight unless you're a gorilla. If the filter is on not more than 3/4 turns and, ideally, has been twisted back slightly in the reverse direction, most should be able to use this method. I like to do it when the filter is slightly warm and the engine cooling down, but I'm not sure at what temperature the filter is easiest to turn.
Loosen:Put a cloth down to catch drip (see 3rd pic). Stand facing against the front part of the driver's side wheel well. I'm 5' 9" and require a short step stool for this. Reach in (see pic) with the left hand and apply torque to the filter. It probably won't move but keep applying torque. Rest if necessary but eventually the filter should start to budge. When it gets much easier to turn, don't remove it but, instead, move into the remove/install position.
Remove/install: Stand facing against the front of the vehicle where the horns are. If you needed a step stool in the first position you'll need it here, too. Reach in with the right hand and get a good feel for the angle/location of the filter. You may even want to unthread it and then re-start the threads to solidify the feel of installation angle. When it's ready to be removed, let it swivel in your fingers to a thread up position to minimize spillage. (Some people have mentioned using a bag at this step. If you can get that to work for you, it will cut down on mess. When I tried it, I dropped the filter so I'm sticking with the pivot method. I've had the skids off a couple of months later and the oil mess is barley detectable.) Carefully pull it out being mindful not to catch it on something and drop it. Wipe your hands and grab the new filter. With the feel of the angle/location of the old filter fresh in your mind, the new one should thread on fairly easily. Turn 3/4 turns after seating and then turn it slightly in the reverse direction to make the next filter change easier.
The downside to this method is having a small oil drip from the skid plate for a few hours.