If there is some sort of awesome quote out there in the world about how to traverse things and getting to places faster... I'd put it here. One important thing to know about getting anywhere in Final Fantasy XI is to simply know how to get to places faster and using whatever abilities you have to get to those places faster. I'm going to mention a few things that you should consider looking into but there are many ways to get to places and it all depends on how much you're willing to spend, to do, and really if you really care for it at all.
First thing's first are the teleport spells. There are 6 teleport spells (not counting the recently added recall spells):
"Teleport - Mea" - Tahrongi Canyon (I-6)
"Teleport - Holla" - La Theine Plateau (K-8)
"Teleport - Dem" - Konschtat Highlands (I-6)
"Teleport - Vahzl" - Xarcabard (H-8)
"Teleport - Altep" - Eastern Altepa Desert (G-7)
"Teleport - Yhoat" - Yhoator Jungle (F-9)
The first three spells can be learned at WHM level 36, whereas Altep/Yhoat are learned at 38 and Vahzl at 42. However, simply getting these spells by themselves won't get you to where you want to go, you'll need to obtain a key item at each of these telepoints in order to teleport to those areas. In case you're wondering: What happens if you have the teleport spell casted on you but you don't have the key item? Simply: It won't have an effect and you won't get teleported while everyone else hit with the spell will. All you will need to do is simply click on the telepoint crystal at the coordinates mentioned above and you will be fine.
Note that the three mainland teleports are level 36, which means it can be subbed at level 72. Something to note about if you want to quickly reach these areas. Not only can you reach these areas pretty fast but it can be a quick shortcut to the Sea and Sky areas... But, that's for another post.
Black mage, at level 18 and 40, can learn Warp and Warp II respectively. Warp sends you straight to your Home Point, while Warp II allows you to send any party member to their respective home point. Leveling your BLM to at least 18 is very nice when you want a quick way to get back to your Home Point from any other nation or places with Nomad Moogles.
If you manage to get to level 40 or so, you might notice some people saying "D2 please." What the heck is a D2? In the Japanese client of FFXI, the spell is called "De-zone II" and D2 is the shorthand of the spell. It has been generally accepted that saying D2 automatically means Warp II and players of all languages understand that.
Black Mage also learns a spell called Retrace at level 55. Retrace is tied to Campaign in the past. Retrace can send yourself or another party member to the nation that they are allied to in the past. If they aren't allied to any nation, it will simply have no effect.
All throughout the mainland of Vana'diel, there are outposts. Each region has an outpost and with a few exceptions, you can teleport to those outposts under certain conditions.
First off, you must do a supply quest to an outpost that you want to teleport to. Once you do it once, you'll have it forever (unless you change nations but it'll be saved once you change back). However, to do a supply quest, your nation must have control of that area. Once you decided what area you want to do the supply quest to, go to any NPC that gives you Signet in your home nation and request to do a supply quest to that outpost. After you get the package, simply go to the outpost and talk to the NPC to finish the quest. You get a few Conquest Points and now it'll be unlocked for teleportation.
Once you unlock a region, you can teleport to there from your nation's Outpost Teleporter NPC:
Bastok - Conrad - Metalworks @ F-8
San d'Oria - Jeanvirgaud - Northern San d'Oria @ D-9
Windurst - Rottata - Port Windurst @ D-5
You can teleport to those regions whenever you want, even if your nation loses control of that region. However, teleporting back is a different story. You can teleport back from those regions back to your home nation but you will be unable to if the beastmen take over the region.
There are also Return Rings and Homing Rings you can buy with Conquest Points from the Signet NPC. All these do will simply teleport you to the outpost of the region that your nation has control over. These items aren't really that great and unless your home point is in Jeuno or something, it won't be that useful at all.
So, there are some small basic ways to get around faster. There's more to cover though, but that's for next time.