It was really tough not having my own space this summer, and not having the money to set anything up at my new place... But, I scrounged together some cash and threw some plants in the dirt.
I started with putting down cardboard on the area that I wanted to use for my first few beds, and I held it down with potted plants. After a couple months the grass stopped trying to fight back and the cardboard lay flat on the ground. By then I had a bit of money, and I bought a cedar board that was on sale at Homely Despot, got them to cut it into lengths, and got some cheap corner hardware to put it all together. Then I filled the center with some hay from my dad, a bag of composted manure, and a couple bags of cheap dirt from the grocery store garden center. It didn't quite fill the box, but I mounded it up on one side and used the other side to trench-compost some kitchen veggie scraps.