Hi Luke, here's a step by step: https://www.southwestboulder.com/blog/diy-dry-creek-bed Its SO cool!
Just dig out a shallow ditch, then line with various sizes or river rock. Can add some decorative rocks for more interest. Don't do it straight, add curves and slight turns. Use a hose or rope to layout. Have fun!
this pin explains it so well https://www.pinterest.com/pin/543809723732457985/
If you have a natural low spot, you can simply remove the grass, put down gravel and then add some larger boulders for interest.
I would imagine you would want to put down a barrier between the ground and your gravel to help prevent weeds from growing up in your riverbed.
Be sure it’s heavy dark plastic like contractors bags and pin heavily with long landscape pins then put gravel, river rock in various colors and sizes then gravel then scatter boulders through out. You can add iridescent glass colored or clear stones scattered on top, face up to beautifully reflect sun. I got semi-precious rocks like jade and amethyst from eBay and put in my real stream connected to my pond too.
Here's some simple instructions