Iudex Gundyr is the very first boss you meet in Dark Souls 3, after waking up in the Cemetery of Ash as the Unkindled. Iudex, by the way, means 'judge' in Latin, which is Gundyr's role: he judges whether or not you're worthy to leave the graveyard and progress to the Firelink Shrine. Your worthiness is, of course, proven only if you can beat his narrow ass. Here's how to do that.
Iudex Gundyr is weak to fire damage. But whence to conjure fire if you're not a pyromancer? Well, the curious and diligent player (or just the player who looks up guides) is rewarded with some firebombs. As you head down the hill from the first bonfire (which you find immediately after leaving the cemetery) you'll see a path continues down and to the left, conveniently towards Gundyr. There's also a path that jinks right and up, almost behind you, before curving down again. If you take this right path it leads you to some skeletons and a dead end, and and the very end of this dead end is a nice little parcel of firebombs. Be sure to equip these in your inventory before the fight, because they don't equip automatically.
This first area is very small, and you'd have to be basically an idiot to get lost in it. Head down that left path down the hill, where the game will teach you about jumping and falling and so on, but you'll see a big, ruined archway a mile off. Head through the arch after cleaning up a couple of skeletons, including one with a crossbow, and there's your old pal Gundyr, kneeling in the centre of a shallow pool of water. Unlike a lot of bosses you don't have to be worried about approaching Gundyr the first time you do it. He's frozen in that position until you pull the coiled sword from his chest, and you might notice while you do so that there's a bunch of dark tentacles growing out of his back. These become relevant later.
Once you've yanked the sword from his chest Gundyr will start attacking you. Since he's the first boss he's not too tough, designed to ease newcomers into the Souls experience, so he shouldn't give you much trouble, and you should save the firebombs for his second phase rather than wasting them here. His halberd has reach on it, but it's easy to roll out of the way of his attacks, whether they're the stabs or horizontal sweeps. He's fond of sometimes vertically smashing it down on the ground, too, which is the best time to run in and get a few light attacks in before backing off again. Gundyr moves slowly, so his attacks are telegraphed quite obviously, but keep in mind that with any of them he can turn on a dime if you're behind him. If you know how to parry then you can use it pretty effectively here.
Once you've gotten him down to half health those tentacles on his back will suddenly sprout into a huge red–eyed slug/serpent/thing which is probably called an abyss beast but ours is catchier, right? Suprise!
Alright, in fairness, the giant slug/serpent/thing probably wasn't a surprise if you watched much preview or network test or streaming footage, but anyway. This is the phase to use the firebombs, provided you still have them, because this is when he's weakest to them (pyromancers should also make good use of their fireball spell).
He can now leap impressively far across the arena if you get too far away, so if you're a ranged or spellcaster type stay ready for that, and watch out for the timings on your spellcasting. If you're melee then second phase has, in theory, 360 degrees of danger: the tail behind, the big slug head in front, the halberd on his right, and a new giant arm on his left. His moves are more difficult to predict in this form and getting a massive great headbut off him will hurt you the most, so stay behind him and watch for the heavy slam attacks to land, because they'll give you more of an opening. Congratulations, you may now enter Firelink Shrine!