Amata,
I am doing this as well. You can get a cheap fluorescent fixture at Home Depot or Menards, and Home Depot also has grow light bulbs at less than the plant places or catalogs, if I recall correctly. I've started seeds under them, this is the first year I intend to overwinter herbs.
I plan to bring the plants in, trim them way back, and put the grow lights on a timer that will give the plants about 5 hours of light a day. Mine will not have any natural light, but I think the key to all this is to put the light fixture up high. When starting seeds you want it very close, and grow lights are a pretty intense light source. I want these herbs (verbena, rosemary, a couple others) to have an environment that more mimics winter--weak sun, short days--than spring.
I also plan to use some capillary matting to keep them moist from below rather than letting them dry out and then get very wet. That will also help me in case I forget to check on them:-)
My elderly neighbor next door brings in her hibiscus bushes every winter and puts them into basically a dormant state in her basement, near a window, but with no lights. They are scraggly when she puts them out in spring, but leaf out beautifully in no time. I've known many an old-timer who overwintered geraniums in this way. I'm planning to throw my scented geraniums under the grow lights as well.
Hope that helps.
Thanks.
Ann