How to level up fast?

I don't think that there is an overly fast way to level up; XP is gained by destroying bandit camps and such, so your levelling is based on how fast you can produce and replenish your armies.

Of course, buying gems using real money might speed things up for anyone who valused their money less than their time

Get a high level acc to invite you to an adventure, you get buttloads of exp

Invite works but you can't start you're own adventure

I don't think that there is an overly fast way to level up; XP is gained by destroying bandit camps and such, so your levelling is based on how fast you can produce and replenish your armies.

Of course, buying gems using real money might speed things up for anyone who valused their money less than their time

XD Lawl

There is no way other than doing all then subquests

Level 14 3rd quest- Complete the "trade as an alternative guest 4 total to level up and don't know what to do

Do adventures with premium time you get loads of XP

Go to http://thesettlersonline.wikia.com/wiki/Adventure_Types and find out what gives you the most for the least.
Tropical sun is an example this is very easy but you can level up a little bit fast.

Spoiler alert the higher the level are the more expoint you'll need so in principle there is no fast way to level up other than to join a gilde and participate in looting.