You can make Fafnir a hybrid, similar to any Guardian, and truly take advantage of his damage potential. I'll note that in Conquest, a more standard support build would be better (i.e., almost entirely defense), but in other game modes, I much prefer building defense and damage.

So, with Guardians, penetration is more valuable than power when it comes to damage. As a guardian, your magical power doesn't scale very well throughout the game, so getting some penetration is what will allow your abilities to dish out the most damage. Luckily, there are plenty of hybrid defense/pen items to facilitate this.

In Joust, Clash and Siege, I'll start with Mark of the Vanguard and T1 boots (or T2 boots in Siege, or sometimes will just go straight into pen boots). MOV allows me to be a little aggressive early. From there, go into pen boots, then Breastplate of Valor. Next, pick up Void Stone. At this point, you have two pen items (boots and Void Stone), two defense items (BoV for physical, Void Stone for magical) and 20% CDR (BoV). As long as the enemy hasn't snowballed on you and/or you aren't behind, you have a lot of bases covered in just three items. The order of your build from this point is largely situational, but you want to round out your build with Dynasty Plate Helm (physical protection and penetration), Spirit Robe (sell for Mantle of Discord when you can afford it) and Gem of Isolation.

Again, Dynasty Plate Helm gives you additional penetration for more damage. Spirit Robe/Mantle of Discord will give you more protections and CDR, and Gem of Isolation will give you more power and health. Most importantly with regards to Gem of Isolation, your allies will be able to apply the passive from that item whenever you buff them with Coerce, so even physical gods will basically get a free Frostbound effect on their abilities.

Obviously, you aren't the tankiest with this build, but you do have some solid protections that will allow you to be aggressive. On top of this, you will have the protections from Fafnir's passive to help out. If you have your ult up and are full health and mana, you can be very aggressive. Your dragon form abilities will do insane damage and you will melt squishies in no time. Since Coerce becomes an AOE buff in dragon form, try to buff as many of your allies as possible each time you use it, because that will give everyone on your team the Gem of Isolation passive. Additionally, you have absolutely insane lockdown potential. Use Coerce on yourself (and your allies), then leap onto an enemy, immediately hit him with your 1, then just hold down the basic attack button and watch them die. You stun them twice in a row, apply a DoT, and continuously melt away whatever remains of their health. The lockdown from the two stuns in a row gives your team more than enough time to follow up as long as they're anywhere remotely nearby.

Something to note: I like picking up Curse with Fafnir. When my ult is up, I'll try to leap into a group of enemies, pop curse and then go into my ult. If an enemy doesn't have an escape or the escape is on cooldown, Curse basically guarantees that they'll take damage from the ult transformation (which is a lot of damage). If you can follow up with a 3 > 1 combo, it is essentially a guaranteed kill. This makes Fafnir a nightmare for squishy gods like AMC, Skadi, Artemis, Ah Puch, and literally any god who doesn't have an escape in his/her kit. If they get caught in that ult AOE, it is game over.

In Conquest, however, going with a more typical Support build is ideal unless you are just stomping the enemy team. The build I listed here won't really allow you to be as tanky as you need to be in a relatively even Conquest round. You could still go pen boots as your lone damage item (which I frequently do), but other than that, straight protections are usually the way to go. You'll still be a huge offensive threat in dragon form, but you'll need to rely on your teammates to secure kills more so than you would with a hybrid build.