Wescott excels by allowing his allies to quickly focus down enemies under the effects of Scrutinize. It would be wise to land an autoattack first before letting your allies use their hard hitting abilities to secure a kill.
Scrutinize has good synergy with the Pickpocket utility mastery as he would require landing autoattacks every now and then at enemy champions to harass them and keep them away from the minions for fear of being dealt heavy damage, thus denying them of the opportunity to farm and at the same time granting Wescott a fair amount of gold.
Scrutinize and his high base damage can help the carry farm but at the same time push the lane. This might open the lane for ganks due to overextension. Coupled by the fact that Pursuit grants a passive base increase in movement speed for all units.
Apprehension is a very powerful tool against the enemy carry or a jungler that has come to gank. Denying them their main source of damage and farm along with decent damage make it the choice for a main skill as increasing its level increases its duration.
Pursuit can be used to hunt down running targets or to help your team initiate a team fight faster due to its active component.
Pursuit can also be used to prevent champions such as wukong from escaping via invisibility as even if they are untargetable without vision your team can still follow their footsteps and deal with them accordingly.
Pursuit makes it harder for enemy champions to shake off an allied bruiser or assassin due to its high movement speed bonus.
Pursuit helps junglers like Udyr and Shyvana that don't have much crowd control abilities or gap closers gank much more effectively.
Getting at least one level of Search grants amazing detection capability to lessen the need for warding the river bush. Given its low cooldown it can be spammed upon cooldown given enough mana regeneration to effectively harass at a safe distance and check if some underlying threats lie about.
Search can be used to catch invisible targets under the effects of pursuit as the hounds can detect invisible enemies even without an oracle or vision ward. The increased movement speed granted by Pursuit can also let them reach their target faster.
Instruct is a very powerful ability be sure not to waste it. Once the enemy has commited to a clash it would be easy for your carry to pick off targets given the enormous damage increase Instruct provides.
It is a very good tactic to use Instruct on your AP carry first and re-leash it to the AD carry after they had thrown their combo.
If the AD carry dies while Instruct is still active, simply re-leash it to the next most damaging ally to make the best out of it as it has a long cooldown.
Be careful of the leash range on Instruct, if your leashed target is being greedy and would warrant sure death. It would be a good choice to cut the line and fall back so you can have the chance of re-leashing it to someone else.
Wescott's abilities lack any solid way of protecting allies and sustain. Investing on a Mikael's Crucible would grant him a way of protecting his leashed target and at the same time solve the problem of his high mana cost abilities.
Twin Shadows is also a good item choice to build your Kage's lucky pick into. This would allow Wescott to gain vision of enemies when search is on cooldown and to further prevent ganks from enemy champions.
Shard of True Ice is also a good choice to get in synergy with Pursuit's movement speed bonus.
Shurelya's Reverie provides cooldown reduction and much needed health to allow Wescott's survival in team clashes. The active component of Shurelya's Reverie can serve for disengaging losing clashes as Pursuit cannot be used for escaping.
Banner of command also works well with pursuit as it can increase the rate of pushing due to the empowered minions being able to move faster down the lane.