I don't have showers at work or school. I do shower in the morning before I leave and try not to hammer into work so I don't get too sweaty. That way I can just wipe down with a washcloth. The key to getting dressed without a shower is to make sure you wait about 10 minutes before you start getting ready so you stop sweating. If you do this right away, you'll just sweat over what you cleaned off
I do keep clothing and shoes at work so I don't have to carry it every day. I take stuff home to wash and swap it out the next trip. It works pretty well. I also carry a comb and deodorant. I use a medium Timbuk2 messenger bag to carry everything I need.
"Only the meek get pinched, the bold survive"