First of all you have to find some dungeons to explore.
For this you can go to the tavern and listen to rumors, or search the map.
Rumors need Diplomacy skill to succesfully find dungeons, searching the map needs either Knowledge or Survival. In each case your skill level tells what DM (Dungeonmaster) level Dungeons you can find.
Another way is to be invited to a Dungeon by another player.
Last but not least you can find Dungeons through player made quests or the daily quests given in the city.
If you have found a dungeon, you will ask yourself "does this dungeon fit for me?"
You can check dungeon properties directly in the dungeon screen.
1: Here you can see the dungeon level and the max npc level. The max npc always is the mainchar, all minions are 2 level lower than him. In some cases player place their followers in their dungeon too, which can vary in level.
2: Here you see the location of the dungeon. If you got the dungeon by quest for example you still have to find it to visit it. For this click on the map 2a to get directed to the right map coordinates.
3: If any buffs are active for the dungeon you see it here. Buffs can be xp boosts or treasure chests.
4: If you like a dungeon you can show it to the dungeon master by clicking the "like star".
5: Here you have the opportunity to send the DM a friend request. If you dont have the location yet and your skills are too low he can invite you to his dungeon then.
Lets move to the statistics button.
Here you easy can see what is more or less awaiting you.
1: Here you can see the single numbers for weaponry, armory, arcane and storage. High numbers mean there are much lootable objects in the dungeon.
2: Here you see the population, aswell as the races you will face against. Many enemies can make a dungeon tough, but mean good xp too.
3: As told before the max npc level determines the overall level of most or all other npcs. In this case you will fight a mainchar lvl 9 and 16 more enemies lvl 7 if no companions are placed in the dungeon.
If you dont stand a chance in a dungeon you can adjust the difficulty level to easy, maybe you can grab some good loot then and come back to go for normal mode with better gear.
The next tab you should check is the Loot.
Here you can check the loot levels for the dungeon. Higher loot levels mean you can find better items. Remember to have at least one party member with a good Search skill and let him loot so you get the max on gold and items out of a dungeon.
Last but not least remember always to check the quests tab.
Here you can see if a dungeon offers quests. This can give you a good gold boost or even superior items. Often quests are followed by others, you can see this if they have a button with 3 points behind them. This quests you get automatically as you finish the quest.