I'd advise against adding sand to clay soil. Essentially, you will turn it into more of a "brick" situation. It wont help with aeration, percolation or infiltration. It will be more prone to compaction and end up making a more solid engineering material than soil. But check your soil ribbon test, feel a bit of the soil with copious
water in the palm of your hand (slippery? silky? sandy?) or you could pay $50 for a soil particle analysis, but not necessary... chances are you are missing silt, but no worries. Then there's also looking at soil structure, is there any? Does it break up into clods, one solid mass or does it look like a stack of plates? all those observations are meaningful
General Solution: Organic matter, Organic matter, Organic matter (OM)... Increasing the soil organics will help alleviate compaction, while increasing microbial activity, worms, infilt/perc... best ways to add organic matter: green manure covercrops (densely planted peas/vetch/grains/radishes, mustards; while still green chopped and churned into soil, or chopped and left on the soil surface and repeat), and two, copious amounts of compost. Careful not to work the soil too wet (it will just ball up) and if too dry (impossible to break bricks)...
I'd start in spring with (keeping in mind soil moisture)... rough up the soil surface, maybe aerate with a heavy tyne fork (without turning soil, try to leave current soil structure), heavy covercrop seed planting and cover it all with an inch or two of good compost. I'd add some daicon radish or a taproot type radish into your cover crop mix that will
root break deep into that soil. you could add a light covering of
straw on top of all of it to help keep the moisture up. Its not an overnight fix and it might take a year or two, but you will end up in a much happier situation. You will have to keep up on your OM additions annually or it will revert, but if you keep up the balance, you will have happy adventures.
Have fun. hope this is useful.