The easiest Dragon to fight is available very quickly into the game; in fact, you can try as soon as you're let loose in the open world. Flying Dragon Agheel is located in the lake to the west of your starting position.
Now, even Agheel is a difficult fight, so seriously, don't just charge in there immediately, it's not going to work out well. In preparing for this fight, we'd recommend you level up to around level 25 at minimum. You'll also want to have some spirits to summon. If you're not sure about how this process works, consult our guide on Spirit Ash summoning.
We also recommend finding some smithing stones and getting a +1 or +2 weapon at minimum. The longer this fight drags on, the more at risk you are. Finally, if possible, get fire-resistance items and gear, as they can provide an important edge.
When you're adequately prepared, head down to the spot marked in the lake on the map above. Agheel will come crashing in and the fight begins. Agheel, like other dragons later on, has a wide moveset, but watch out for the following attacks in particular:
If you're in singleplayer, we highly recommend using Torrent, your horse. Agheel rapidly flies around and uses wide arc whenever they breathe fire, so being mounted allows you to run past attacks that you otherwise have no hope of dodging. If you're playing in co-op, things are trickier, as you won't be able to summon Torrent. Your best bet will be to use the rubble in the lakebed to try to provide cover from when Agheel breathes fire, but this isn't foolproof.