This guide will explain several methods of getting yourself to Wintergrasp and Dalaran before NPCs will teleport you, and without using another person to do so. Very low level characters will die during the trip, so be sure to remove your weapons and armor if you do not want a significant repair bill in the end.
Getting to Wintergrasp requires the player to die at least once in order to get onto a mountainside that leads into Wintergrasp. A major advantage that allows for players to reach Wintergrasp is the use of the swift spectral gryphon when you die, despite being at a lower level.
Please refer to the accompanying map to get to the spot where you will need to die. The quickest way to get through is by following the red path. Essentially, you will need to go to the south side of Ymirheim. From there, there will be a path up to the top wall surrounding the Icecrown Citadel. You will then need to go to the west tower (Cathedral of Darkness), and then along the south walkway to the rock face (marked in yellow). Once there, there are three accessible ways to get up the rock face a bit: one on the left, one in the center (the rock jutting out onto the walkway), and one on the right. You will need to get up on the left side, which will end up going out and over beyond the walkway edge. You will only be able to go up onto the second rock (which comes up to the edge of the walkway), but that is all you will need. Then, using a ranged attack (if you don't have a ranged attack, you will need to aggro the Glacial Bonelord, and then run back up to the spot), attack the closest Glacial Bonelord to you in order to aggro him and kill you. You will want to go up onto the third rock up (to the left) and as far back as you can in order to get the farthest reach when you rez again. After you are dead, fly your gryphon up over the rock where you died and as far south as you can rez. You should be now on the mountainside facing Wintergrasp. From there, you will be able to go to the mountain's edge and fall into Wintergrasp.
An alternative to going through Ymirheim (marked in green) is to go along the bottom around to the north of Ymirheim and then south through the gates, but there are many more mobs along that route so it will take longer.
As a third alternative - recommended for characters of low level: If you happen to die in Icecrown, fly with your gryphon over the southern edge of the area, near the Cathedral of Darkness. As soon as you leave Icecrown, you will lose your ghost gryphon, but you will be in Wintergrasp - now all you have to do is let a spirit guide at a graveyard - best is of course the one north of the Fortress - rez you. Welcome to Wintergrasp!
If you head south and go south past the dragons in Ymirheim, then follow the snow, you will come along this pathway up to Icecrown Citadel. Use the path marked in red to do so.
Going up the slope from Ymirheim. You may need to jump a bit to get up it, but not much effort.
On south walkway of Cathedral of Darkness. Three paths shown that could be taken. The one that you need to take is marked in red. You will also notice the Glacial Bonelord on the left you can aggro later when you get up on the rock.
Once you're on the "second rock", you should be able to range aggro the Glacial Bonelord from the edge of it... otherwise you will have to aggro him as you're comming up to the rock. Once you do, run back up onto the third rock and wait against the rockface to die (shown in red).
Once you fly back to your body, there are 2 spots you will be able to spawn (both marked in red). Also shown is where your dead body will be (yellow circle).
If you follow the rockface along the left after you resurrect again, you can actually go down a gully that leads into Wintergrasp and probably survive.
(Horde only) During the quest [72] Blightbeasts be Damned!, you gain control of a flying mount which can only be summoned in Icemist Village, head towards the northern most point of Icemist Village and fly up and over the frozen waterfall. This is where you can get access to Lake Wintergrasp. Keep flying straight north and 10 secs later, you will automatically dismount and parachute down into Lake Wintergrasp. (You must be at least level 71 to take this quest)
(Alliance or Horde) During the quest [74] On Ruby Wings (requires level 71), you are given a [Ruby Beacon of the Dragon Queen] which enables you to summon a Wyrmrest Vanquisher which can't be used everywhere in Dragonblight, but in finding the place closest to Wintergrasp, you can fly up to the "ceiling", and then fly toward Wintergrasp. Start at the 'corner' in the Dragon Wastes that is north-north-east of the Ruby Dragonshire, where the scar that delimits the Dragon Wastes has a corner. Fly up as high as you can, point your dragon towards Flamewatch Tower (you should see it on the minimap), and charge forward. If all goes well, you should just cross the zone boundary when you get dismounted. From there, you should parachute into Wintergrasp! (Note that you will land in an area populated by level 80 mobs, so be prepared to make a quick getaway.)
In order to get to Dalaran, one must use the portal inside Wintergrasp Fortress. The only problem is that you will need to have had your faction's side win in order to gain control over the fortress. In the main, central area, there is a "defense portal" up on the stairs to the Wintergrasp keep door. Using that, you will be teleported to the room before the Vault of Archavon instance. From there, there is a portal on the left to the Violet Citadel and then you will be in Dalaran.
Previously, you could travel in ghost form to Dalaran and resurrect there using the Spirit Healer. This no longer works as of Patch 3.3.3 and you will be ported to Crystalsong Forest.
Take the ship or zeppelin to the appropriate faction holding, either eastern or western Northrend. Since the Cataclysm, everyone has the flight route to Dalaran from those locations; it costs 2g to get there, but portals in the faction headquarters or a hearthstone ensure a free trip home. (The full trip of both legs should be taken at least once before appropriate level; the views are spectacular.)