Adventurer is a skill rewarded by completing set of dungeons, the list can be checked by visiting Lord Gandalf at the main town Crendale.
As you complete a set of dungeons you will be rewarded a bonus experience in Adventurer skill.
Other than dungeons, there are certain monsters that gives Adventurer experience, these can appear during Gathering, Prospecting, Lumberjacking or Fishing. If you manage to kill the monster from the Random Events, you will get 100 experience in Adventurer and some resources as drop.
Daily reward can be claimed at Lord Gandalf. The higher a player's Adventurer level is the more likely the reward rates increase.