Since you have never been to Sea Serpents Grotto or Norg and they have added Home Point Crystals since I originally drafted this answer in 2014, it will be in your best interest to check out the FFXIclopedia.org page that lists all the HP Crystals and try to hit all the ones that will be in your path as your travel to Norg. The is a HP Crystal just inside the entrance of Norg that will make traveling in the future so much more easier for you. Please see link directly below for link to page.
Directions to Sea Serpents Grotto
There are 3 ways to get to Sea Serpents Grotto and Norg, 2 of which I think will be open to you if you have never been there. One is Yuhtunga Jungle in the Elshimo Lowlands. That can be accessed either by way of Kazham or thru Tele-Yhoat, which is located in the Yhoator Jungle at (F-9.
If you come by way of Kazham, you will need to go to (E-11) to zone into Sea Serpent Grotto. This does involve being able to wind your way around the different paths thru the jungle to make it to the zone at E-11 and can be quite frustrating. There is no map that is pre-marked to show you the path. The mobs in the jungle will aggro if you are lower level and some will aggro a level 99. Some players have no problems with the jungle map, I've always found it to be a pain in my ass. I always preferred to come in via the Tele-Point or even easier the Out Post. Now that there is a Home Point Crystal inside Norg all that drama is in the past. Beware of Tonberries. Here are the links for the main pages for both jungles:
The 2nd way would be if you come by way of Tele-Yhoat, you will need to make your way west, until you zone into Yuntunga, then continue west until you zone into Sea Serpent Grotto at E-11. Of course to come by way of Tele-Yhoat you will have had to traveled to the Tele-Point and touched the crystal in the past to be able to port in.
The 3rd way is sort of important to check on - check to see of your nation has control of that area or not. If they do, go to a gate guard, one of the guys with the initials after their name and pick up a supplies package for Yhoater Jungle Elshimo Lowlands. You know you will be getting close to your zone when you see an open field and an Out Post on the left hand side. Trade you supplies to the Out Post guard if you nation is in control - you will be able to come by Out Post after doing that.
Next step is you have to drop down one of the holes in the ground. Straight out in front of the outpost you will see a very LARGE hole that the lip of it is slightly elevated - that is the hole you want to drop down. Take the left hand passage, then you will have another smaller drop and you will be on a little meadow area with a LOT of fish-dudes. Head towards the back (E-11), under the waterfall. You will zone into Sea Serpent Grotto.
Directions to Norg (after zoning into Sea Serpents Grotto)
Hug the right wall all the way to Norg. You will come to a point where you are off the map - stay on the right wall. There will be a blank door, just click it to open it - if you are a low level, just about everything in here WILL AGGRO and they hit hard. The zone for Norg is at (F-2/F-3) 06:28, March 16, 2014 (UTC)