First thing: try to keep your chain clean. It may be greasy, but it should not have excessive dirt on them and the chain should not be black with road grime. It might mean that you wipe down the chain the night before every other ride, but its worth it. I use a dry lubricant, oil based to wipe down the chain the night before the ride.

Any auto parts store like Kragen will sell a box of disposable gloves. In the summer, your hands get sweaty and its nearly impossible to get the gloves on if you're in a hurry to change a flat and get back on the bike. So the next thing you need is a dry cloth which you can get at Kragens as well. I wipe my hands dry before using the gloves. The cloth I tuck half in the bike shorts and half sticking out. They're the cheap red one's I think from India or Pakistan.

When I don't use the disposable gloves, I use that red cloth to handle the chain.