Passive - Doom 'n Gloom
Doom - Periodically, Vex becomes empowered by Doom, causing her next basic ability to interrupt dashes and Fear enemies.
Gloom - Whenever a nearby enemy dashes or blinks, they become marked with Gloom. Vex’s next basic attack against a marked enemy detonates the mark, dealing bonus damage and refunding part of Doom's cooldown.

The extra damage provided by gloom marks is extremely useful, try to hit enemies marked with gloom whenever possible. Also remember that Doom only procs on basic abilities meaning that Shadow Surge will not consume the fear.

Q - Mistral Bolt
Vex launches a wave forward, dealing magic damage to enemies it passes through. After a short delay, the wave accelerates but has reduced width. Mistral Bolt detonates Gloom on any marked enemies it hits.

This ability is your main source of quick wave clear since it costs a mere 45 mana early. It'll take some time to get used to the bolt going from wide and slow to thin and fast but once you have that quirk down it becomes an extremely deadly ability all on it's own.

W - Personal Space
Vex gains a shield and emits a shockwave, dealing magic damage to enemies around her. Personal Space detonates Gloom on any marked enemies it hits.

Personal Space is going to be your self peeling ability. Using it while your doom passive is ready makes it extremely easy to escape a bad situation. I suggest taking this second into champs such as Yasuo rather than taking Looming Darkness second.

E - Looming Darkness
Shadow flies to a location, increasing in size as it travels. On arriving, Shadow deals magic damage, slows, and marks enemies hit with Gloom.

Using E is a good way to get an aoe ranged fear on the enemy team. Using E before Q for wave clear also increases how fast you clear the wave by a substantial amount.

R - Shadow Surge
Shadow flies forward, marking and dealing magic damage to the first enemy champion hit. Vex can then recast this ability to have Shadow pull her to the marked target, dealing additional magic damage.

If the marked target dies within a short time of taking damage from Shadow Surge, Vex can cast Shadow Surge again within a few seconds.

Shadow Surge is what makes you a threat. The initial damage is laughable but the secondary impact does a lot. This ability provides a lot of risk and reward since Vex does lack backwards mobility, be careful when using it.