You should teach yourself how to adjust it, since it's an important skill and is easy to learn. Lots of articles on the web about this subject. Tony Athens @ Seaboard Marine in San Diego has written about it and has articles on his website last time I looked. He also makes a great stuffing box. A subscription to boatdiesel.com is worth it for browsing the forums and learning others' opinions about this and other important subjects (their prop calculator is excellent).
Short answer, the box should be dripping regularly (a drop at least every few of seconds) while under way @ cruising speed. The box should be adjusted to allow this drip while the boat is actually cruising, since trying to adjust it at the dock doesn't give you a clue about what will happen when the shaft is warmed up and spinning. This obviously requires someone to drive the boat while you're down in the bilge with your butt in the air. You should have enough drip to keep the stuffing box cool to the touch while cruising. Otherwise the shaft can score from the friction and that's the first step toward a broken shaft. Tony runs in his boxes on a lathe and then installs grease fittings on them, so that you can adjust it under way for the right amount of drip and then hit it with a shot of grease at the dock so that it doesn't have to be tightened down when it's sitting for long periods. Dripless shaft seals sound tempting because you don't have to learn all this stuff and pay as close attention to them. After researching and thinking about it, I bought a regular stuffing box from Tony.
Re-packing can be done in the water but should be done on the hard. You pull out all the old packing (there is a sharp corkscrew like tool for this available at places like West Marine) then wrap a section of new packing all the way around the shaft. Cut the packing so that it fits all the way around the shaft exactly, with no overlap and no gap. Cut three or four pieces of the the same length and then install them so that the gap is 120 degrees apart for three sections and 180 degrees apart for four sections. Install the packing on the shaft and then adjust it as mentioned above. Make sure you get all the old packing out, it can be hard as a rock and it's easy to miss the last piece at the bottom of the stuffing box. Make sure you have the right size packing, if not confident about it take a piece of the old packing or, better yet, the shaft and stuffing box to the place where you buy the packing (unless you have an eight foot long, 100 pound shaft). There is new type of packing that lasts longer and works better than the old waxed flax. May want to pull the shafts and rudders for inspection at the same time. This can be easy and cheap (except for the cost of going on the hard) or hard and expensive, depending on how long the shafts have been in there and what kind of couplings you have. There are tricks for getting stuck shafts out, check the web before you get out a cutting torch.
The tricks didn't help me much. I had to cut off both my shaft and rudder and have new ones made. Fortunately I found a machinist that was reasonable and a new shaft and rudder were not too bad. The peace of mind alone was worth it, as both the 40 year old bronze rudder and the who knows how old stainless shaft were badly scored, which made adjustment of the stuffing boxes more difficult. I think jb914 was charged fairly and gives good advice on costs, but this is a DIY job with a little care and research, unless your time is worth a lot more than mine.
