The link that SailingDog gave you gives you all the instructions and pictures you need to do this job yourself. It is easy after you have done it once and is well worth the peace of mind to know that it is good to go another 5 - 10 years. The stuffing box is supposed to drip while turning and even somewhat while at rest. Have you tried tightening the bolts to see if you can minimize the drip? If tightening the bolts slows the leaking down to a drip then you can think about replacing the packing the next time you haul out (which is the best place to do this the first time, IMHO).
BTW, the replacement GORE GFO packing (that Mainesail, er, Halekal36 recommends (as do I) should only cost you about $25 + shipping. I got mine from here: Virtually Dripless Packing by Gore GFO
All you need is a pair of wrenches, a razor blade and some determination to actually work on the stuffing box. It really is pretty easy if yours is a typical installation.