Dig out a hole as large as you can without harming adjacent plants' roots much, at least a few inches wider and deeper than the plants current root system (presuming you started them in pots). When transplanting, mix into that as much brown organic matter as possible.
In other words get that heavy clay soil out of the hole and add things like peat moss, composted leaves, pine needles, coffee grounds, even sand if nothing else. Till up that mix really well in a bucket or tub to the point where when it is barely damp it doesn't clump together.
When transplanting the plant into the hole, sprinkle that down into the hole around the plant but keep it loose, don't pack it down. Make it a bit of a mound that will settle over time from watering or rain.
The point of the above is to help the plant get a root system started so as it gets larger it is better able to penetrate the clay soil and less in need of frequent watering, can be watered less often and deeper each time.
At the end of your growing season, throw your yard waste like leaves, lawn clippipngs, etc. into the clay soil and till it up along with any crop plants you'd otherwise throw away. You could haul that sort of stuff over to a compost pile or bin then back again later but if it's tilled into the soil then nature will take care of that for you.
As journey11 mentioned, do mulch. Get some of the really low quality

cheap shredded bark mulch that's half rotten away already. It will turn into topsoil faster and every year you add it, your ratio of clay goes down.