I am a male, here is what I do:

I work in a hospital in which we wear scrubs that belong to the hospital, so I really don't have to worry about carrying clothes with me. My commute is currently 19 miles one way.

Since it's wintertime here in South Texas, I really don't sweat much at all on my commute to work, provided I wear the right amount of clothing for the weather. I always take a full shower before going to work, and once I get to work, I usually arrive to the locker/changing room about 30 min before everyone else so that I'll have time to wash up and eat breakfast. I usually go into the men's room, strip down, and give myself a little sponge bath, going over and areas where I've sweated with a wet soapy cloth, rinsing with a wet cloth, and then drying with a dry cloth. I usually put on a little bit of mild deodorant when I am done to take care of any lingering smell. So far, I haven't gotten sweaty enough to require a full shower; when it gets warmer out and I do, I'll find out which hospital ward has a staff shower room (mine currently doesn't) and use it. (My job as a nurse requires my being in people's personal space on and off throughout the day, so it's important for me to not exhibit any unpleasant odors).