You only have 3 activated abilities, meaning you have less to worry about, But the cooldown for those feels very long considering how often you Auto attack.
I put one point in each ability for the first 3 levels and then level Piercing Arrow
and Blighted Quiver
back and forth getting levels in Chain of Corruption
as soon as they are available. I max Hail of Arrows
This skill shot is a bit different as it is a charged shot but can be released early. It gains dammage and distance as it chareges and you can move slowly while chargeing, but moving while charging is not the easiest thing to get the hang of. It will pass though all enemies damaging them pregreessively less as you hit more enemies so you might as well just shoot through the minions and enemies rather than shimmying to the side to get that extrta damage, in my experiance while you are moving into position the enemyy is usually getting away. I get Piercing arrow first and max it alongside Blighted Quiver
This is a great passive ability, giving extra initial damage up to 3 times and bonus damage if you strike the enemy with an activated ability they are damaged more for each blight point they have. Maxing it second alongside Piercing Arrow makes your auto attacks that much deadlier. The blight points only stay for 6 seconds but if you miss the chance to trigger them dont fret too much as you can apply more for free rather quickly. This is great for picking up Minion kills early game, as well as good harassment.
Your Second Activated ability, this is more utility than a real damage dealer. It places an AOE, causeing arrows to rain down dammageing anyone in the area, and then blights the ground for a few seconds slowing anyone in or moving into the area. Great for placing behind the enemy causing them to rethink their retreat or slow them long enough to pick up the kill. remember that the arrows will hang in the air so if you want to land it on a moving enemy then you will need to learn to lead them a bit. It seems to hang in the air the same amount of time no matter how far you are shooting the arrows, making it a very fast attack. Get one point at lvl 3 and 1 more point at lvl 10 then max it last.
Your Ultimate and last activated ability, It greatly damages the primary target and immobilizes them. It can then jump to additional champions, damaging and immobilizing each enemy champion in range once. This is great for several uses. Locking an enemy in place for your team or yourself to finish off, or if you are lucky, laying a large amount of damage to the enemy in a team fight. Don't be afraid to use it on a single enemy if you think they will get away, but do try to save it for team fights if you can. Hitting teams with this is fun and powerful but doesn't always work, people are quick to jump away from their allies if they are infected. But even if it doesn't jump to more champions here it is still useful, causing the enemy to blow its flashes to avoid the effect is a good consolation prize. It is also important to note the effect continues after you die so if you are going down locking your killer down to save your team mates is worth the use.