I'm Sp12 -- I write guides here and can be found streaming at http://www.hitbox.tv/sp12; if you have any questions/comments feel free to post at either.
This is a set of builds for Phantom Assassin, one of the stronger laning carries (especially in a 1v1 or 3v1 setup) with incredible stat growth and chase potential. She is not hard to understand mechanically but takes strong decision making and early last hitting to use effectively.
She is a great laner, with a semi-escape, ranged last hitting or harassment tool, and decent early EHP. Dagger is why she's one of the best chasing/zoning/laning carries -- it's spammable harassment/last-hits/slow/vision. You should aim to win the laning stage with this hero.
Each build gets its own minisection for you to check out, so consider this an anti alt-tab guide. The formatting for this guide is matched heavily with my Faceless Void guide, which you can check out if you play him.
PA is probably the weakest of the "traditional" hard carries -- not only in her scaling but also her winrate, which is just over 40% across pub skill brackets and competitive play. You shouldn't play her as a hard carry unless you are sure you have the team and game for it -- meaning lots of disables and buffs.
I'm not going to list out skills/whatnot -- there's a well-maintained wiki, great replays, and even video guides on how to play her. An easy way to get better is to watch replays on player perspective -- filter recent games for PA and very high skill level.
Guides are suggestions not demands. On almost any of the builds I will offer you choices, and rather than repeating analysis on how to make that, it's all here.
Treads or Phase:
Both of these boots are good choices, treads offer attack speed so you're not entirely reliant on Phantom Strike, extra HP (which gets amplified by her good armor and evasion from Blur, and tread switching to help alleviate her mediocre int growth. Phase give extra chasing (or escaping!) as well as some early damage. Treads are better for DPS at almost any point in the game.
HoTD (and?)/or Vlad's:
They offer comparable lifesteal, damage, and armor, but HoTD has a better upgrade ( Satanic) and active while Vlad's has mana regen and pushes better, at least until you bring in a HoTD creep.
HoTD is probably more versatile -- get a speed creep for running around the jungle, frost armor creep for soloing Roshan, centaur creep for teamfights, satyr for pushing -- whatever you want. Plus, having the creep stand back a bit gives you an assured phantom strike target for escape. You can stack with it. You can have it go pressure a lane a bit. You can have it deny runes or scout jungle.
Vlads is more teamfight oriented and suggests an early basilius and pushing. Make sure not to have multiple on one team.
Mana regen: / / / :
PA is probably at her worst at level 1 -- no escape and Stifling Dagger is mediocre until level 3. Play safely using your tangos and Stout Shield to endure harassment as you work towards a PMS+regen item. Once you have those (around level 4) it's very hard to force you out of lane without a gank or major outplay given your escape and high physical HP.
So farm but know when you can go in. PA is one of the best carries at helping supports shut a solo offlaner out, and once you hit 6 a surprise crit can turn an engagement around fast.
Once you can farm jungle you can push out your wave then rotate into jungle for farming/split pushing, and once you have all your laning items you can start moving with your team abusing your very early rise in power, but be careful of magical damage as nukes are a very large percentage of your HP and you won't have a BKB. Your basic combo with Stifling Dagger + Phantom Strike (reversed if they're in range for a blink strike and have no stun) followed by autoattacks.
If you went Battlefuryyou should be farming and split pushing (when safe) a lot more as you contribute little in teamfights compared to a PA with Medallion of Courage or Vladmir's Offering or Drum of Endurance. Conversely, if you went early game items you can grab a bfury if they have an illusion carry.
Notice how simple that is. That means that most of using PA effectively in small teamfights is knowing when and on whom to go on. In general go for anyone that "could" die if you get a crit in your first 3 attacks from Phantom Strike or anyone with strong burst. Do not go in first (typically) and try to plan who you would blink to to escape if the situation suddenly changes. Towers are not that scary for you given your high armor and evasion.
Take Roshan after winning a teamfight as PA is quite capable of soloing given her high HP and evasion to avoid bashes/hits. In fact, you can do it as early as level 7 if you get a fast HoTD and take an ice troll creep.
The supports you were once blinking on and instakilling now have ghost scepters or Force Staffs and are avoiding you -- that's OK, PA is a good manfight hero, especially with basher. Wait for your initiation unless you can BKB+ Abyssal Blade and blow someone important up for sure. Remember your squishiness to nukes and BKB appropriately in teamfights. PA should rarely be on her own at later stages in the game given her mediocre escape and split push without battlefury, but against some teams (without BKB penetrating disables) you can abuse BKB+TP to get out of bad situations.
You invest a lot into early aura items -- be sure to be there for the important teamfights. Vlads gives a ton of pushing power early along with the sustain and armor.
You invest a lot early into armor -- you can afford to go BKB next to make yourself very hard to pin down with magic immunity and 20+ armor/evasion at 25 minutes. The frost creep and alpha wolf both let you take Roshan solo.
This build focuses on stats heavily to avoid a BKB for games where there are many sources of magic damage but not much disable or where a BKB would prevent you from carrying effectively. Your illusions can crit and evade and you have great agility gain, so manta is quite strong on this hero.
You are a deadweight but not as much as other Bfury carries -- you must leverage an early lane win into an early battlefury into many items.
Blame your team.
Just kidding, consider whether your laning situation was appropriate. Not having strong lanes or lanes with a realistic farm priority (PA and Void in one lane?) can end your game before it really starts. On the other hand, if you went offlane trying to do the traditional BF build no wonder your game wasn't stellar. If every lane but yours lost then even great play by just you can't always win the game. If you or your team made a major mistake (5-man Reverse Polarity?, no antipush into a Luna+Furion+Pugna?) that can cost you the game. It's actually really good to think about why you lost a game afterwards as it forces you to adapt. You can check out replays in your game history.
There are 3 varaitions of a modern PA build along with the traditional bfury one. If you have any questions/comments/criticisms feel free to post them. At the very least I'd like a comment why if you feel like downvoting :P. If you feel it was worth the read a vote up helps get builds seen more.