Let me start by saying, I hate to weed. Yes, I know that if you do it after a rain, that it's easier. But I still don't really like to do it, so I've used a combination of methods to avoid it.
First, I send my rabbits through the aisles to eat the grass as low as possible. In the past, I have used ducks to eat and trample it. I'd like to say that I meticulously planned my rows to accommodate the repurposed dog kennels that I use for grazers.
That would be a lie. I'm just not that farseeing. Generally, I kind of bumble along and things tend to fall into place. As you can see, Rodgers is pretty happy to help.
My Silver Fox rabbit, Rodgers, grazing. Buck named Rodgers. Get it?
After the grass is low, then I lay cardboard down over it. I avoid any cardboard with coating and color printing on it. Since the tape doesn't breakdown, I remove it as well.
Flattened cardboard that I got from the school I used to work at.
Once the cardboard is situated, I put mulch over top of it. Now, to be honest, I have a nearly unlimited supply of mulch, as my husband has a tree removal business. It isn't pretty, but it does the trick. I don't know if it would be cost prohibitive to use this method if you had to purchase mulch. I guess it would depend on how much you hate to weed.
It keeps down the weeds quite well, though you will need to keep a watch out for pests that may like to live in the mulch like mice, rats or voles. I have four cats who keep them under control.
Even though it's not dyed, it's free. And that makes it beautiful!
If you want to plant full-sized plants in the mulch, just scrape back the mulch and use a sharp instrument to cut the cardboard enough to dig a hole in the dirt. After planting, just push the mulch back up around the base of the plant.
Over the season, the cardboard breaks down, adding bulk to the soil. While I doubt this method would be a useful method for a really large garden, it works great on my tiny suburban homestead.