I concur with the other posters:
1) Shower regularly, wear anti-perspirant (not deodorant). Sweating is more of a "gross" thing than a "smelly" thing if you're otherwise clean.
2) I prefer loose-fitting, short-sleeved, button-down shirts similar to "Hawaiian prints" when biking around town on errands. They're thin, loose, and dry very quickly. "Quick-dry" synthetics can actually create a smell once they've been sweated in. That smell doesn't go away without washing. Cotton tees get wet with sweat and stay wet for the entire time I'm in town. They don't smell, but I'm not comfortable wearing a wet t-shirt indefinitely.
3) Slowwwww down. Ride at easy conversational pace. This is actually hard for me (and likely some other folks as well). I like to ride to get where I'm going and find out once I'm there that I sweated more than I intended. Riding slow intentionally is not easy.
4) Rack, trunk bag, panniers, basket, bike trailer--whatever is necessary to keep from wearing a backpack.
5) Route--I hit a few neighborhood streets and greenways more often when it gets hot. A little more time, but it forces a slower pace and is more shaded.
6) Timing--Save your main errand days for days when you can get out and back in the morning. Save one-off errands for evenings after work (and it's light outside longer to help with this during the hottest months).
Commuting? Totally different since I always shower/change for that.