Some things I have learned is that the right size packing is very difficult to get into the packing gland, and that pounding the pieces flat with a hammer helps a lot.  That little bottle of green colored packing lube (comes in a 35mm film container) is very helpful in not only getting the packing in, but also in keeping water out etc.  I have also used the dripless packing (green putty like things that you mold with your hands down to the right size to essentially replace the center ring of packing.  I have also found that it is difficult to get all of the packing fully into the gland which can leave much more thread exposed than you are comfortable with (as may be your case). 

It is not a big trick to do your packing with the boat in the water.  The bilge pump will easily keep up with the flow.  In addition, if you get to the point where you need to go to west marine or something, simply shove a ring of packing in the nut and put it back on the shaft, it will stop the flow of water (this way you can stop efforts at any point, although you want to make sure the job is done right before you run the boat). 

Back the nut off, and if you wish, you can tie a rag around the shaft to abate the flow of water from a small spray to a heavy drip.  Then make sure the nut is completely empty of old packing.  Cut three lengths of packing the correct length, or two rings and molded no-drip stuff if you are using it.  Use a small hammer to slightly flatten the rings of packing.  Then use lots of that green grease stuff (I have seen it at West Marine) douse the packing ring in it and push it into the nut.  Use a small tool with a blunt end (not sharp) the end of an allen wrench will work, to push the ring all the way into the nut by tamping all around.  Then do the same with the subsequent rings making sure that the splices are not lined up.  If done correctly (and with the correct size packing, you should now be able to get the nut on the shaft with a comfortable amount of thread, although no where near maximum.  Tighten the nut by hand until it is just snug, and then using large channel locks or a packing nut wrench, tighten down the locking ring.  At this point, turn on the engine and put it in gear.  After a short time, if the gland is warm you may have put the nut on too tight, a little warm is OK.  After several hours of running, you will probably notice more dripping from the gland, at which point you need to tighten up on the nut a little until the drip stops with the engine off, this is to accommodate running in of the packing.  After this initial adjustment, only periodic adjustments will be needed as the packing wears.