I'm a SWEATER! If the ride is longer than 2 miles I'll be sweaty when I get there. Luckily I have showers at work but I ride other places they aren't available and have luck doing this. Keep in mind I'm a big fat fatty who is prone to being sweaty and smelly so if these tricks work for me they'll work for anyone. :-)

Like everyone else stated a normal shower at home is a prerequisite. I scrub everything super awesome style and then get dressed for my ride. For a commute style ride my choice is gym shorts, under armor underwear and a performance fabric type t-shirt. I DON'T PUT ON DEODORANT AFTER THAT SHOWER. I find it's easier to clean a sweaty armpit at my destination that isn't covered in goup. When I arrive at my destination I try to take a 15 minute cool down. Then I hit the bathroom for my washup. Not sure what your hair situation is but I keep my head shaved so I don't need to worry about shampoo or other hair stuff. If you're a gorilla like me some light manscaping helps too. I'm not talking an olympic swimmer shave here I just run the clippers over my whole body every 10 days or so to keep all that hair under control instead of letting it become a bushy sponge to absorb funk. I bring shower shoes, 2 washcloths and a small towel with me. One cloth is my "soapy" cloth and one is my "rinse" cloth. First I just use my wet hands to squeegee sweat off everything and continually rinse them in the sink. Then I get my soapy cloth wet and use some of the bathroom hand soap remembering that the more soap I use the more I need to rinse off. Soap is only there to break the surface tension of the water and a little goes a long way. I wash myself in zones using the soapy cloth to wash, wet hands to remove excess soap, and finally by clean cloth to do my final rinse. You can keep wetting and ringing out both cloths in the sink. When all is said and done I dry off with my towel, apply some deodorant and a spritz of cologne or body spray. This whole process takes about 10 minutes and when I'm done I'm every bit as clean as I was when I got out of the shower earlier. I stand right in front of the sink most times and could care less if anyone walks in. If I'm someplace where discretion matters, like a bathroom that is busy and a father may walk in with his young daughter, then I'll use a handicap stall to be more discreet. In that case I'll bring a collapsible dog bowl or collapsible camp sink with me to use as a basin for fresh water and wring out my cloth into the toilet. I pack my wash cloths in 1 qt zip lock bags. The bags can be used as place mats on the counter so you have a clean place to set your cloth down while using the other one. Then I pack the wet cloths back in them for the ride home. I bring a dry stuffsack with me and put my shower shoes, sweaty clothes and towel in there so it's not nasty putting them back in my bag. For the ride home I just wear my undershirt and normal cotton underwear under the gym shorts and adjust that with layers based on weather. I'm in GA so I'm not often trying to stay warm on a ride. I sweat so much that except for the gym shorts I could never think of wearing the same clothes home I wore to ride in. Hung up to dry or not once they come off I'm not putting them back on. For a 10 mile ride at commuting pace I don't think bicycle specific clothes are anywhere near a requirement. I have a comfy saddle on my commuter bike so padded shorts aren't needed.