I feel very strongly about the superiority of permanent-no-dig garden beds. Yes these are strong words I use here, but it's just where I stand. No dig gardens have so many benefits, but one of them is how easy they are to make. Here is a brief how-to.
You start with cardboard or news paper; it blocks the sun and kills the grass. The grass starts to decompose (as does the cardboard) and invites worms to feast. The worms provide their highly valuable castings to your garden bed. Be sure to overlap the cardboard otherwise grass will start to come up through the cracks. Appliance stores are a great place to find HUGE cardboard boxes.
You then add a couple of inches of decomposed compost. This is what the plant will grow in. You can contact your extension service for good local sources.
On top of the compost you add "the mulch" - again a couple of inches. Straw was available but you can also use fall leaves (run them over with a mower the get them decomposing faster) or even shredded paper. This adds a layer of air and decomposing materials that create an ideal environment for beneficial micro-organisms.
On top of the mulch you add again more compost, enough to completely cover the mulch and any cardboard peeking out.
Give it a little smoothing and you're ready. Really.
Your first season, deeply rooted crops like roots may not grow well because of the cardboard, but after a season you should be ready to seed carrots as well. For plants like tomato starts you can cut a slit in the carboard and drop the roots into that.
I have been been using no-dig permanent beds for 5 years now and I find them very easy to maintain. I find it even more managable to cover and mulch the paths between the beds as well. This kills the grasses and weeds right next to the beds and prevent them from entering the beds. But if you are planing on leaving grass between the beds I would recomend mesuring your lawn mower and designing your beds to make mowing easy.