my run is nearby my fenced garden, and I don't have a direct "connection" setup right now. I just open the door and shoo them into the garden. Then when i want them back in the run, i shake the can of treats at them and throw some in the run.
I actually let mine have time in my garden all summer once plants were established and they were pretty respectful of it actually. they sampled some things like tomatoes and blackberries, and helped out tremendously with the bugs, but (oddly) stuck to the paths for the most part.
If you want them to be able to come and go on their own, you could do a tunnel or just setup some poultry fencing to make a path for them into your garden. If your garden is not covered, then there's no point in going to the work of making the path from run to garden covered either.