I took a bus from dublin on the "wicklow tour". Any of the tour buses that take you around Dublin have brochures for this kind of day excursion. It stopped in some other places on the way and was a nice way to see some of the counrty side.
Wicklow Mountains National Park is located to the south of Dublin. You can go there by car. If you do not have one, take a bus which you can catch in the center of Dublin in the morning (in 1999 it cost L10-L12 - return ticket). Unfortunately the whole trip lasts only about 5-6 hours.
on foot of course and nobody should complain...