My first time through the process of establishing my garrison I was quite unhappy with how long it took me. It seemed like I was doing something wrong. I really wasn't, but I could have done it faster if I had been less distracted. I've enjoyed wandering around and doing quests in a less than optimal fashion the first time though, but if I'm going to build more than one garrison, I cannot do the same on multiple characters.
Taking notes as I went along I have determined the bare minimum of quests that you need to do in order to unlock your level 2 garrison.
**Note, I have only done the horde quest lines. I have not leveled any alliance characters yet.**
The first step is of course to go through the Dark Portal and complete the Tanaan storyline. Make your way to Frostfire Ridge and establish your garrison. Do the quests presented in your garrison until you have rescued Olin. After assigning Olin his first mission you should get the quest to rally the Frostwolves in Wor'gol. From this point the following quests need to be completed.
Rally the Frostwolves (follow this chain through Moving In)
Gormaul Tower
These Colors Don't Run
Deeds Left Undone
(Honor Has Its Rewards can be skipped)
Great Balls of Fire
The Butcher of Bladespire (this kill rewarded me with quests for my primary professions)
To The Slaughter
Armed and Dangerous
Last Steps
Moving In
Save Wolf Home (continue this chain through Back to Bladespire Citadel)
Free our Brothers and Sisters
The Farseer
Pool of Visions
Back to Bladespire Citadel
(Ga'nars Vengence can be skipped)
Securing the South (continue chain through Strength of Our Bonds)
(We Be Needin Supplies and Ashran Appearance can be skipped)
They Who Held Fast
Of Fire and Thunder (might be optional)
Into the Boneslag
Moving Target
The Strength of Our Bonds
Where's My Wolf (and followup Enfilade)
Enfilade
The Master Siegesmith
Return to the Pack
After you go to your garrison and turn in Return to the Pack you should have the quest Bigger is Better from Gazlowe. BAM level 2 garrison and plans for all your level 1 profession buildings.
I've read that reaching level 93 will also trigger the ability to get the level 2 garrison. I completed all of these quests and was barely into level 91. These quests didn't take very long and I ended up building my garrison so quickly that I don't have the resources I need to build structures. Oops.
Doing the quests for your professions will open up that blueprint ahead of getting to the level 2 garrison, but I believe they only drop for production professions that you have (requiring a minimum of level 1 skill). So if you are a double gatherer, your choices are to level to 93 or do this quest chain.