To start with, this is what most of my backyard looks like... dandelion fields forever!
Over the winter, I'd thrown out some of that mammoth bale of hay, and sprinkled some field peas into it, in the area where I wanted to start a bed this spring. (Field peas are a "cover crop" that you can put into an area that you've already planted to re-nourish the soil.) Before I started this day, John had made a 6'x3' rectangle of 8" deep boards around the hay/peas area. (He got some treated wood before I could say that it wasn't the best... and then after some research, it seems like it's really ok as long as I put some flowers around the edges. I'm thinking marigolds.)
Removed the hay/peas, and stapled in some weed guard fabric.
Replaced the hay/peas.
Mixed together 2 bags of compost, and 2 bags of organic potting soil. Spread it around!
Since the backyard doesn't get a ton of sun, I decided to plant mostly greens back there, and some peas. My starts are beginning to grow INTO the lighting system, so I needed to get them out ASAP! (That's why there are 2 rogue squash plants in there; ok only one is in the picture.) Going to plan for marigolds around the edges (to soak up any tiny amounts of chemicals that might leach into the soil) and some sugar snap peas to fill in any gaps in the corner.
Use the fact that you have random yard debris everywhere to your advantage! (I used a branch and several rocks to keep the row cover down.) Floating row cover is useful in weather like this, as it keeps the soil a few degrees warmer, keeps out birds and many bugs, and lets rain in!