How do I build a terraced garden on a hill of rocks on a budget?

You will have to collect the rocks from around the area. As big as you or someone stronger can carry. Start laying them in a line, whether straight or curved. If need you may have to cement them. Make sure the wall is thick as well, and just keep on adding to till you have the height and width. Regars George

https://www.pinterest.com/explore/landscaping-a-hill/?lp=true

I would determine where I'd like to have a small terraced area or two...then clear a 6-10" strip of land of the rocks...then as mentioned above make a stacked rock retaining wall not too tall...or used retaining wall block for two or three layers...filling in those "found" rocks in the back of the retaining wall to hold back the erosion even more. Every winter I have more rocks heaving upwards...I like them along the sides of the walking path...or the swale that helps keep the water a bit directed where I prefer. I used the leaves in the fall as well behind the wall to hold moisture and eventually turn to soil...Good Luck

I would make the retaining walls using 4x4 posts where you want the levels to your terrace. Make wire cages from chicken wire or fence wire and place the rocks inside. Clear any other rock from the level that you don't want and add soil to landscape as you wish.

You need to remember to start at the bottom and build up from there. I've used RR ties, but that's much more involved: chain saw, rebar, industrial size drill w/long bit, sledge hammer, etc.

thank you

In addition to working from the bottom up and the terracing, you asked for a garden. It would be best to go with a 'container' concept. Make boxes the size and depth you want, slip a good weedblock type material in them and attach it before you fill it. That'll prevent the dirt from draining away when it rains. Then you can plant whatever it is you want: flowers, veggies, groundcover.