Find Siegward's armour and get him out of that well.
Dark Souls 3: Siegward of Catarina
The "onion knights" of Catarina return in Dark Souls 3. You'll first meet Siegward of Catarina when you enter the tower in Undead Settlement. Leave the area (or die) and return and you can meet him on the hidden middle level. From here, you can join him to fight an optional boss, scoring the Toast emote and a cask of Siegbrau, which can be traded with the crow at Firelink Shrine, by chatting with him afterwards.
If you'd like to continue Siegward's quest beyond this point, make sure you send Greirat on his first scavenging trip as soon as possible, as it seems to be linked to Siegward's quest somehow.
Your next encounter with Siegward takes place just outside Cleansing Chapel in Cathedral of the Deep. If you don't find Siegward in the well immediately, spend a few hours clearing out Cathedral of the Deep up to the second shortcut, but no further. If he has not yet appeared by this time, and you've already done everything previously listed in our walkthrough, go spend a few hours grinding or farming in earlier regions, and come back. He should turn up eventually.
When Siegward does appear in the well, you'll learn he doesn't have his armour. You can purchase this from Unbreakable Patches for about 10,000 souls total. Patches can be encountered further into Cathedral of the Seep or at Firelink Shrine; see his entry for details. Return Siegward's armour to him in the well before defeating Deacons of the Deep to advance the quest.
Meet Siegward again in Irithyll of the Boreal Valley. From the Distant Manor bonfire, look for a room leading off a small sewer near the lake. Exhaust his dialogue.
You'll next find Siegward in Irithyll Dungeon. Look for a pit full of rats (careful, they respawn) near a sleeping giant and speak to Siegward through a window. To rescue Siegward, start at the Profaned Capital bonfire and look for a blue peaked roof on a house in the swamp. Look from this roof to the stairs to spot an open window you can leap to. This leads to Siegward's cell.
If you complete Siegward's quest up to this point, he will join you for the boss battle against Yhorm the Giant, pretty much winning the fight for you. Speak to him once more after the battle and exhaust his dialogue. Siegward dies shortly after the Yhorm the Giant fight. You will receive the Catarina armour set and a second Stormruler as a result.
Note: image above is fan art of Siegmeyer of Catarina. We weren't able to trace the original artist. Please get in touch for credit!