To walk between the rows you normally create walkways, which can be bare soil, inlaid stone, bark or even concrete. In our case we made wooden plank boards, which tend to stay cleaner (less muddy) during or after a good rainfall and which slugs, bugs and thugs don't seem to like to hide under.
Some people put straw or wood chips down either in the walkways or raised sections, but we advise against it. The reason is that these make ideal beds for slugs, rodents and insects. We prefer to give them no place to hide: simply black plastic with some wood boards as walkways. This system has worked well for us over the years and we have gotten used to it.
Once every 3 years or so, we gather up all of the wood walkways and spray them down with a waterproofer, something like Thompsons Water Seal. This keeps them basically water repellent and the bugs won't go near them, but the worms don't seem to mind so much.
Treat the boards every few years
Finally, the walking boards help to hold the black plastic down during high winds and prevent it from ripping. We have never had the black plastic rip to any significant degree while the walking boards are in place.