How do I build an easy rain water recapture for my side hill?

not that it would be easy ... or inexpensive, but a stone berm/wall with support on the 'down' side might work -- or if the slope is not too steep, you could hire a landscaping contractor to build a pond .... would still need to control over flow --- water is probably the most difficult to work with .. amazingly powerful, heavy, and has a mind of it's own.... this is one case where Gravity is NOT always our friend!

Not sure what you are aiming for.... a water catchment basin to capture the water? A water tank? How steep is the hill? Are you thinking swale or pipe to direct water? There's lots of different ways to capture water, so we really need more information.

We found the easiest way to capture rain is from the roof of our home. We put gutters down to barrel level and fill the barrels off the rain gutters. We used NEW garbage cans and cut a hole in the lid to tight fit the down spout into it. Also for extra needed rain water we connected other barrels for over flow save from the first barrel to at least one or two more. What's more this was repeated on both back corners of the house with a total of 4 or 6 barrels full of rain water. It gets us through dry spells even for our orchard of apple, plum and peach trees. Hope this helps. No mosquito troubles with the lids intact. Hope this helps.

Here's some ways it's done in my state we have Monsoon rains with terrible flashfloods so many of the systems stop flash flooding provide catchment systems. You could use one of the terracing ideas and then use french drains into regular drains to remove water into holding tank/pond/stock tank at base. Don't know how big slope/area is but terracing doesn't have to be a major construction project. Native Americans used it also to irrigate grow crops. https://extension.arizona.edu/sites/extension.arizona.edu/files/pubs/az1564.pdf

Lynn Sorrell thank you so much for this information it was amazingly helpful.

Cynthia