Leveling up in Gekkeiju Online™ is experience point based. This means that you'll be able to advance your character as you gain experience points. You can gain experience points for example by killing monsters or by solving quests.
Once you have made your way out of Greentree Inn you'll find different kinds of monsters around. You can attack the monsters simply by left clicking them once to target them. You'll automatically keep attacking your target as long as your in attack range. If you have offensive skills or spells you can also use those in combat at your target. Right click on the target-window if you want to untarget.
You should start with level 0 wurms that are right next to the Greentree Inn as they are relatively easy to kill.
When you manage to kill a monster it may drop some loot items. You can pick up those items by clicking them with left mouse button. You can also use the Get Nearest Item-action to do it if you have it in your quickslot bar.
A very important thing you need to do always after killing a monster is to dig a grave for it. You can do this by using your shovel item when you're near the corpse. If you fail to do this in time then the corpse may raise as an aggressive, very strong undead that will attack and, in most cases, kill you. It's a very good practice to assign your shovel to one of your quickslots for easy usage.
Quests are a very easy way to get experience points. You'll have several quests available to you in Greentree. Just talk to the NPCs to get the quests. You can read more about your quests in the Quest-tab of Character Details-window.
Different quests will require you to do different tasks. For example a quest may require you to talk to someone or kill some amount of some monsters. Once you have done the quest requirements you can talk to the NPC that gave the quest to get a reward.
Level advancement isn't automatic as after level 10 you'll be able to use your experience points to train skills and spells instead of levels. To advance your level you'll need to talk to a Level Trainer-NPC. In Greentree the Level Trainer is inside Greentree Inn, just next to the exit.
After advancing level you'll get 25 stat points that you can use at the Level Trainer to train more stats. The cost of stats depends on your race and character class.
During the first 10 levels you'll learn new skills and spells every time you advance your level. At level 10 you'll no longer get skills but start gaining Free Guild Levels which you can use to join different guilds.