In this game is only one set... the dragon set
King Kelp Dunatrim, the Dwarven king in the Dwarven Halls, is going to tell you about the legendary Dragon Armour. If you can find the breastplate and a certain gem called the Heart of the Dragon, he says Grischa, the Dwarven smith, may be able to reassemble it. The breastplate is said to be in the possession of one of the rich merchants in Verdistis.
First of all, you have to bring Dunatrim a note (that proves his brother's (=Gregor in Glenborus) involvement with the stolen Axe of Stone issue) from the dungeon in the Dwarven Halls. Else, the quest will not even be triggered. To get the note past the guards at the entrance to Dunatrim's throne room, you have to throw it inside, get stripped off all your belongings by the guards, then pick up the note again once you're inside.
After the king has assigned you the quest, you should go to Sir Patrick in Verdistis for the breastplate. He wants you to go and collect Lucius' debts (a guy in the farmlands) before telling you more about the breastplate. The quickest and most convenient way to solve Sir Patrick's quest is to pay Lucius' debts (=2.500 gold).
The dragon heart can be obtained from the Warrior's Guild in the Dark Forest. You have to complete their 2nd quest to get the heart (from the Imp fortress).
When you have both items, you should go to Grischa, the Dwarven smith in the Dwarven Halls and let him forge the Dragon Armour. This will take him a day so make sure you have a sleeping opportunity nearby.
Once you have picked up the Dragon Armor, you should go and see King Dunatrim again. Throw the dragon armor past the guards and enter the throne room. Pick up the dragon armor inside, present it to the king and get your reward (the helmet of the dragon set).
You can now go back to Grischa and buy back the dragon heart (useless) or the original breastplate. The latter may be potentially useful. My breastplate had some skill boni which were not included with the dragon armor piece. Me "stoopid" thought that the dragon heart would just add some boni to the breastplate but keep the original enhancements <img src="/ubbthreads/images/graemlins/winkwink.gif" alt="" /> . Looks like I was wrong... - Seriously, the dragon armor piece itself may turn out to be worse than the breastplate so it might actually make sense to buy it back from Grischa. Just see for yourself...
BTW, the complete dragon set consists of a lot more items. The shield can be found in the armory of Stormfist Castle (SW section of the castle). If you have already been kicked out and didn't take the shield with you, you can go back by throwing your teleporter stones past the guards (far into the castle's yard). This is not supposed to happen, of course. So don't talk to anyone. Just go to the armory, pick up the shield and leave as if nothing had happened.
The belt of the dragon set is in an abandoned house in Verdistis. You will fall through the floor tiles in that house. The belt is hidden away in the basement.
The gloves can be found in one of the elven burial grounds (southern part beyond the elven village on the Dark Forest map). There is only one hive of burnt wood & debris that can be highlighted and clicked. The gloves are in there.