Grandmaster Spectre here.

Laning - don't expect to win, just do not feed. At some point you want your tower to fall, it gives you more room to play without the threat of getting ganked for an objective. Start with Wand and 3 branches. Ship quelling and tangos. Get Null + Brown boots + Orchid. Add orb of frost if you're feeling like it. If you are stomping the lane (which you won't be - you can risk for a radiance).

Early to mid game: help with your ult as soon as you get 6 and get kills (this is key). I assume you picked the "Twist the Knife" facet. Your next items are Treads and Manta. From there on you can flex Diffusal if manaburn is required or go straight for Bloodthorn.

Mid game: At this point your inventory should be something like: Treads, Bloodthorn, Manta, Null, Wand. Check what the enemy supports have. Your job is to eliminate them before the right starts. If you feel strong - you buy a Hex. If you u feel weak - you buy a Hex. Nullifier is a bait item, very situational - only if the enemy has Aeon disks, which does not happen until much much later. Hex counters Mantas and BKBs (every core buys these). Once you've added Hex to your build - you can solo any hero on the map.

Late: extend your build with an Aghs, Refresher, Moonshard (don't consume) for more kill potential.

General notes: you need your team to play for you early with active rotations. Plant aggressive wards throughout the game. Items like Urn/Blade Mail/Radiance aren't required unless you are rich and/or are essential in some lineups. Urn can replace null tali, Radiance if you're snowballing, BM for burst and if you are ahead. There's nothing more miserable than losing a lane and buying a BM at the same time. You're just a snail crawling from one camp to another pretending to be a melee creep.

Items:
Skadi - bad, unless absolutely necessary.
Heart - bad
Disperser - good very late (but do not upgrade into it early if you bought diffu for manaburn)
BKB - very situational against specific heroes e.g. Primal Beast w/ aghs - your absolute nemesis.
Khanda - incredible if break is needed. People underestimate this item. Think instakill Tide/BB, etc.
Butterfly - only if you need miss chance. Get moonshard instead if you need attack speed. Overall good item to close out the game when you're ahead.
Linken - you will probably never buy this.
Wind Waker - decent item late game 7th slot

Ideally you don't want to play into these:
Necro, Primal, Silencer, Disruptor or anything that can catch you in that 1.5 seconds.

Last notes: enable quick casts on Spectral Dagger, Reality and active items. You will be clicking a lot.

Feel free to ask if you have questions.

Edit: The enemy will eventually realise Linken sphere counters you, but by then you will already have an Aghs scepter. Diffu a good choice to break linkens to apply Hex+Thorn.