Always be aware of how much Rage you have gained. You don't want to turn Berserk too early, or too late. If you have too much, use your abilities particularly Vent Anger, to reduce your Rage- you can also reduce your Rage if you cast abilities without hitting more than 1 enemy (enemies include gods, minions, and monsters). And if you have too low Rage, look for 3 enemy minions to use Barbed Spear and Salmon's Leap against, to gain rage quicker.
In solo lane(and in the jungle if you can manage to go berserk at level 2 at a good time), you have huge kill potential at level 2, since you will have enough Rage built up at this point, so that you can use both Barbed Spear and Salmon's Leap onto the minion wave, and transform into your Berserk form, granting you huge early kill potential. Even if you don't get a kill at this point, you will have the pressure advantage in lane. However don't be over-confident, you can still die if you aren't careful.
Another huge kill potential opportunity is once you hit level 5. At this level, you will have your ultimate, and if you have enough Rage built up, you will be able to dump your whole kit onto an enemy, and kill them. Do make note that you will end up losing more Rage than you gain if your abilities do not hit multiple people- keep this in mind before you jump into an enemy, use your ultimate on them, and end up not having enough Rage to go Berserk.
Spear of Mortal Pain, your ultimate, will grant you crowd control or CC immunity for 1 second, when casting this ability. This can be very helpful if you're in the middle of the enemy team and the enemy support is ready to stun you. HOWEVER, know that War Cry, your ultimate in Berserk form, does not grant you crowd control immunity.
Don't be fooled by Furious Charge, Cu Chulainn's dash in his Berserk form. It does not stun- it only knocks back enemies.
Cu Chulainn's basic attacks, similar to Awilix and Bellona when using Scourge, have longer range than most melee gods. This can be very helpful to know and can aid in trading or boxing in lane from a safer distance.
Take some time to learn where you can and cannot use Salmon's Leap from. Certain walls may be too thick for you to leap over. Knowing what walls you can and cannot leap over can help in escaping, ambushing, and ganking.
Once you go back to your normal form, Barbed Spear and Salmon's Leap will already be off of cooldown since your Berserk form lasts for 20 seconds. Keep this in mind as it can help you land a kill with the extra cast of Barbed Spear or you may be able to escape with Salmon's Leap, right after reverting to your main form.
It just takes time, and practice when it comes to Cu Chuliann's Rage.
When I plan on Raging-Out I typically like to do it when
When I don't plan on Raging-Out, and I seem to be close to it...I typically pull off and cast an ability, usually
I know this isn't the most thought out post in the world, it's just kind of hard to put the Rage-Management into words.