>> Rick/Corey I've no problem with areas I'd be happy to allow runoff to fill. But how to get the water to cooperate? Install some kind of underground irrigation system? That seems impractical, to say the least.
The conventional answer 50 years ago was to dig a big, deep ditch and bury some kind of pipe, like un-fired clay "tile" pipe, deeply. Then back-fill the ditch with many cubic yards of drainage gravel.
Now people tend to use perforated corrugated plastic pipe, like 4" or 6" in diameter, in smaller ditches.
That's still crazy-expensive or a huge amount of work.
I just dig a narrow trench and don't even back-fill it. My clay is so hard that the sides have not crumbled in 4 years.
But here's the hard part:
The bed itself must not trap water, so the clay "floor" of the bed needs to be dug and scraped fairly uniformly to slant toward one edge or one corner. That way, water IN the bed will drain away toward that low corner.
Dig and scrape that "floor" of hard clay so that it drains to one spot.
Now visualize a straight line from that lowest corner to the low spot you want to drain TO.
Presumably that line passes through some clay. That's the clay that would have trapped the runoff. That clay needs to be removed so that water, running always DOWNslope, has a path from the bed to the low spot that never requires water to lift itself UP and over any clay.
A slit trench or ditch needs to follow that line. If it's long and/or deep, you might need power tools and/or assistants to help excavate and move the clay somewhere.
Once I get it roughed out, and have dug most of the trench, I like to wait for a heavy rain. Water is easier than a laser level or tight string for finding the high spots and low spots. Once the trench floods behind a high spot, I dig out that high spot and let the water rush down to the next high spot. Also, a little water softens clay so it is easier to dig.
I'm finished when even a heavy rain leaves no deep puddles in the ditch or the bed. Then I COULD install perforated corrugated pipe and drainage gravel ... but now I don't. I just make the ditch as narrow as possible and risk breaking my ankles. If you have clay SOIL instead of clay CLAY, you might need to back-fill with gravel or something to keep the trench from collapsing. One tip: plastic perforated corrugated irrigation pipe is much cheaper and MUCH lighter than an equal volume of 3/4" gravel!