The info below is a bit out of date as it refers to the beta. If you happen to be looking for an up-to-date reference for your Dragonknight, I suggest this manual. It includes some killer advice on leveling up, builds, skill rotation, and gold farming.
The Dragonknight class in The Elder Scrolls Online will be one of the strongest solo classes in the game. It might even be the strongest solo class in the game. This is due to the combined killing power, AoE potential and survivability powers of the class. Dragonknights will be able to swap between two weapons during combat which will help them when it comes to choosing how to initiate combat and how to survive when under pressure.
To play the Dragonknight solo, you will want to choose a build that provides plenty of killing power but also a strong dose of survivability, crowd control and/or self-heals. This class has a particularly easy time with choosing a build that suits this combination since each skill line focuses on one of those elements. The Ardent Flame skill line is suited for straight DPS but also does a large amount of AoE DPS. This makes it extremely useful for soloing. There will be many situations where you’ll want to kill more than one enemy at a time.
The Draconic Power skill line is the tanking skill line, but for Dragonknights who are pure soloers, you may wish to take advantage of some of the tanking active abilities and passive abilities while solo. Many do not require the use of a shield. There are even a few self-heals in this tree. The final tree, the Earthen Heart skill tree, gives Dragonknights some interesting options for crowd control, survivability and group buffs that might be useful.
As far as choosing which abilities to use while solo, you will want to focus largely on DPS abilities from Ardent Flame and mix in a few others that compliment those well. You may wish to use a sword/shield for your secondary weapon set in order to have a setup that can survive well under pressure or you may wish to equip a secondary DPS weapon along with some crowd control abilities for when the going gets tough for your better eso leveling experience. Either way, you will want to focus on DPS but also have ways in which to avoid combat or survive a beating from multiple groups of mobs.
It may also be a good idea to equip a bow or staff to utilize some ranged abilities. Ranged abilities often help speed up combat while solo due to the fact that many mobs do harmful AoE abilities that can be difficult to soak while in melee range. It’s also easier to tag mobs as ranged.
The info above is a bit out of date as it refers to the beta. If you happen to be looking for an up-to-date reference for your Dragonknight, I suggest this walkthrough . It includes some killer advice on leveling up, builds, skill rotation, and gold farming.