How do I level up my dragons as a beginner?

Your dragons have two separate progressions — don't confuse them:

1. Reign Level: it rises through combat (XP comes from enemy troops killed) or by feeding your dragon Meat. It raises the dragon's 4 stats and the max size of its army. ⚠️ It resets with each new Reign.
2. Star Rank: it rises with Relics at the Hatchery. It's permanent, makes the dragon bigger and stronger, and unlocks new Habits.

As a beginner: fight regularly to push your Reign Level (which serves you all season), and stockpile Relics for stars (which stay forever). Hit tiles, beasts and Hedge Knights for the XP.