Directions to Ballsbridge (From Galway)??

Least complicated, with just two turns(!), is to take the N4 the whole way in up to the R111 (South Circular Road), turn right there (big junction, watch the signs) then follow the R111 the whole way around to Baggot Street and turn right there (just after the Mespil Hotel and a Maxol station). Continue straight to the Lansdowne Road end of Ballsbridge. After that, I don't know where in Ballsbridge you're going

This map shows the Dublin end of the route. If you're at all nervous, I strongly recommend you take a close look at the first turn. It shouldn't be hard, but it's not an entirely normal right-turn.
http://maps.google.com/maps?f=d&source=s_d&saddr=chapelizod+bypass&daddr=Grove+Rd,+Dublin,+County+Dublin,+Republic+of+Ireland+to:pembroke+road,+dublin&hl=en&geocode=%3BFfK-LQMd9VKg_w%3B&mra=ls&sll=53.333231,-6.278858&sspn=0.049717,0.154495&ie=UTF8&ll=53.337331,-6.287956&spn=0.049712,0.154495&t=h&z=13

Was going to respond but then saw that AndrewMc has given you the perfect route.

Just to say, the section after the turnoff is a good few miles (approx 3 I'd say) so don't worry if you think you're taking a long time. For most of the route, the canal will be on your left. The Maxol is very noticeable as it's on it's own on your left with no buildings before it. The Mespil will be on your right, just before the Maxol.

Also, don't worry. If you can handle Galway drivers you're more than able for Dublin drivers who are far less erratic and even display some knowledge of the rules of the road. You'll be fine.