Spectre is a powerful carry but is weak early and highly farm dependent. If you're going to pick him, make sure someone can babysit you early on and your team ganks or pushes down other towers when your lane is pressured. Mid game, you excel at finishing off escaping heroes anywhere on the map, and late game you are a tough to kill DPS hero. Unlike a lot of other carries, you create a unique AoE presence in team fights that shines with the right team composition. You're also slightly more versatile than other agility carries because Dispersion allows you to be effective with HP items in situations where your team already has enough physical DPS.
Strength: 19 + 2
Agility: 23 + 2.2
Intelligence: 16 + 1.9
Damage: 46 - 50
Attack Animation: 0.3 / 0.7
Damage: 46 - 50
Casting Animation: 0.3 / 0.51
Attack Range: 128 (melee)
Sight Range: 1800 / 800
Decent early stats overall, but low agility gain and high strength gain relative to other agility carries.
There are some variations to Spectre's skill build depending on how the laning phase is going. You almost always want to max Spectral Dagger first since it's the only way you're going to be doing anything in a fight, and once you get Haunt you can help your team net at least one kill with a quick Reality + Spectral Dagger. If you're skilled enough to know when you should not max Dagger, you probably don't need to be reading this guide.
The main variation comes from picking between Dispersion or Desolate after level 7. A level of each is picked up before then because Desolate works with Haunt and Dispersion helps your survival while farming during the laning phase. The jump from level 0 to level 1 is pretty big (+10% on Dispersion and +20 on Desolate), while following levels provide less (+4% on Dispersion and +10 on Desolate). Depending on how much you're being harassed/ganked versus how much you're ganking, you will generally want to increase the more relevant skill past 1 before the other. If you're forced to play very defensively and can't get an early Vanguard, you may even want to get stats early since 10% -> 14% on Dispersion is not a big increase when your HP is fairly low.
Haunt is your most important skill but has a fairly long cooldown, so half the battle is knowing when to use it, and furthermore when to use Reality and who to use it on. Sometimes it's pretty obvious, such as when Tidehunter lands a great Ravage and the rest of your team is going in to follow up. You usually want to Reality next to a disabled target who you want to eliminate first. Also, try not to target someone who is closer to their allies than to yours, so you aren't focused to death before help arrives. The final use for Haunt is to escape from a gank when you have no other options. Quickly press R and follow with D on an illusion in some other part of the map near a lone hero that can't finish you off. Generally, it's preferable to use a Town Portal Scroll or Spectral Dagger to get away, but in some cases those aren't viable or are on cooldown.
Spectral Dagger has the rare capability of allowing you to pass over normally impassable terrain, much like Batrider's Firefly. It can target ground or enemies, damaging anyone it passes through on the way and leaving behind a trail that you can walk on no matter if there is a cliff or a tree. Sometimes it's more effective to use it to go over hills rather than to directly hit an enemy, especially when escaping or chasing later in the game once you have Diffusal Blade and plenty of damage. The finer points and ideal timing for using Spectral Dagger as well as Haunt can only be learned from experience, but playing it safe is your best bet if you're newer to Spectre.
Radiance is a core item because the passive damage aura functions on your Haunt illusions. It gives you a larger presence in team fights that most carries don't have and functions well with Dispersion since in order to stop your damage they have to kill you and thus take more damage. In team fights, Haunt+ Radiance will make a huge impact on the squishier heroes and cause trouble in general. Of course, the +60 damage is also nice once you enter the fight and start beating on some poor victim.
Vanguard is the first item you want to get because the bonus health and regen let you farm without worrying about being harassed or dying to ganks. It also provides more EHP on you than most heroes because of Dispersion. If you are farming very well and their team is ignoring you, you may want to just get the Ring of Health or skip it altogether, but it's a risky move that you should only try if you're experienced.
Always get Power Treads because you're a DPS hero that already has a global presence with Haunt and unitwalking (and more) from Spectral Dagger. If you think you can get Sacred Relic without upgrading your boots, you may want to do that.
Diffusal Blade makes ganking a breeze because of the purge active, and as a bonus, the illusions from Haunt get the mana burn orb. If you can't farm a Radiance and/or your team needs some real help early, you might want to get this first.
Manta Style is perfect for Spectre because you already make 5 illusions with Haunt and they work with Desolate, Diffusal Blade's mana burn, and Radiance's burning damage. The same goes for your Manta illusions, so at this point you should be tearing up the other team in big fights and easily picking off any stray heroes.
If the game is still going, Heart of Tarrasque or Black King Bar are probably your best bets. HoT makes you extremely difficult to kill and Dispersion becomes immensely powerful while BKB's magic immunity can make or break some fights and it does give you a bit of HP and damage. You should already be doing solid amounts of damage and someone else on your team should be carrying Assault Cuirass. The only time you should get a Butterfly is if you're dying to a lot of physical DPS heroes with no Monkey King Bar, because the evasion does not trigger Dispersion. Likewise, if the other team has a difficult to kill carry with Butterfly that you find yourself fighting often, that's the only time you need a Monkey King Bar. If you seem to be surviving fights but not getting kills and the other team has squishy heroes dishing out lots of damage (like Outworld Destroyer), thats a situation where you might want a Blade Mail. However, Heart of Tarrasque and Black King Bar are still viable options. Certain heroes like Lifestealer will chew threw your HP with Feast so that is a case where HoT may not the best option, but then BKB is great since you can kite around him (or through him with Spectral Dagger).
Most of this was covered in the skills section, so I'll go over what your goals are throughout the game and when you should be doing certain things. First of all, don't pick Spectre if you already have a hard carry that needs babysitting. That is the only place where you can function well. You also need a lane partner that doesn't need farm to be effective, such as Lich or Warlock.
In the laning phase, focus on last hits until you can get Ring of Health and are level 6 or 7. At this point, you need some map awareness so you can Haunt and finish someone off if your team needs your help. You can ask your team to ping when they may need your ult as well, but you should still make the decision on whether or not it's worth it since you won't be farming when you're ganking. If you can get at least 1 kill that your team wouldn't have otherwise, then it's a good idea. Also, the vision and minor damage from Haunt is sometimes enough and you don't need to use Reality + Dagger, allowing you to continue farming instead of jumping somewhere else. Avoid dying.
Mid-game is basically an extension of the laning phase, where you should seek out farm and gank when it's worth it. By now you want to have Radiance because bigger team fights will be happening and the burning aura will turn fights in your favor. Once you have Diffusal Blade as well you should be getting at least 1 kill each time Haunt is available, so let your team know if they are sitting around being boring when you're ready to go. Avoid dying.
Hopefully by late game you have an advantage in terms of farm so you can start wiping out the other team and pushing down towers. Avoid dying while you can finish your items and keep up the map presence to scare your opponents into sitting around in base while you continue to farm. Ideally, you have a good initiator so you don't have to do it, but if you need to, you can. In the worst case scenario, try to have money for buyback and try to save Haunt so you can instantly return to the fight if you die while initiating.
Lifestealer can be problematic because Rage nullifies Dispersion and Spectral Dagger while Open Wounds and Feast makes your high HP beneficial to him. Try to kite him and don't attempt to 1v1 him. Use Diffusal Blade's purge to help get away or Spectral Dagger through trees/over cliffs to evade him and find a different target. Obviously, if using Haunt, don't Reality next to him.
Heroes with very high mobility like Storm Spirit or Anti-Mage are not worth chasing around unless your team can hit them with a silence or stun. If your team can't keep the important targets in place, focus on heroes with the least escapes first and you should get kills.
Early in the game, you need a solid ranged babysitter that doesn't need farm. Other than that, Spectre works great with almost every hero in the game because he has global mobility like Furion and his Spectral Dagger is excellent for chasing. If your team has a ganker in the middle lane, that's fantastic, but if not you can still get kills in the other lane by making a 2v2 fight into a 3v2.
Later on, any stray hero that someone on your team finds can become food for you. Ideal team fight allies are the standard AoE disables that let your Haunt images lay down the beating - Tidehunter, Warlock, Jakiro, Sven, Lina, Sand King, etc.
While Spectre isn't picked as much anymore due to the current metagame and has been nerfed many times, he is still an excellent late game option. In a gank heavy team that can pressure the opponents while keeping their carry safe, Spectre can make an excellent complement that other carries would not. Knowing when Spectre is a worthy pick is important in high level games, but he's great at all levels if played properly. Watch replays and practice to get a sense of using Haunt and Spectral Dagger to their best potential, and you can become a powerhouse carry while still having a large presence across the map all throughout the game.