Speak to your Dungeon Master about taking a Cleric or Arcane based spellcasting class. Rise to the appropriate level and cast either Planar Shift or Dimension door. Doing so will allow you to access the Astral Plane. You should be mindful of the random encounter rate based on time, and that Githyanki pirates are a common occurence in the realm.
You can also do this as a non spellcasting class by locating the correct Portal and succeeding in forcing it to operate, a la "Stargate" style. It helps to have a few scrolls of Analyze portal to be sure you've found one that wont send you into somewhere like The Abyss or Fire Elemental Plane.
Happy roleplaying.