Undying has quickly become one of my favourite heroes. This is due to how ridiculously easy it is to win games as him. With a good Undying on your team, you've already won every 5v5 teamfight, broken highground, and defended every push. Undying is the God of teamfights, and if you're losing, you're doing it wrong.
Ring of Protection is magical indeed. You will build it into Tranquil Boots (stay with me), but if you're going to get an Urn of Shadows, you can get the Sage's Mask first and build a cheeky temporary Ring of Basilius. If this confuses you, rest assured that this is some next-level stuff. Disassemble the basilius once you have more gold -- this is most effective when you are doing badly in lane, and urgently need an item.
Blight Stone is great, increasing the damage the enemy takes by a tonne in the early game. You can build it into a Medallion of Courage, if you're feeling it. It stacks with Orb of Venom, and together with Tombstone they equate in a won lane, usually.
Tranquil Boots are the only boots for Undying. You'll be fighting so much, these boots will heal you quite quickly, so you won't have to waste mana on Soul Rip healing yourself after fights. Undying has a 2.8 int gain -- more than his strength. He has plenty of mana, Arcane Boots is redundant. Phase Boots for chasing makes sense, but ehh. Tranquil Boots gives you more.
Urn of Shadows is hilariously good, get it if nobody else on your team has it and you're doing well early game. Remember to use it on enemies fleeing on low health.
Aghanim's Scepter is the item for Undying. The earlier you get it, the more devastating it becomes. If you're doing well, start going for it after boots or urn. (I always get Staff of Wizardry first, for mana).
Blademail is very strong, get it before aghs if you're doing badly. Decay gives you more health and the enemy less, and Soul Rip can heal yourself quickly. Blademail is therefore perfect, especially for use against enemy physical damage dealers.
Necronomicon is a sweet all round item for Undying. Some games it works better than others. I generally treat it as a post-aghs item, it's great against squishy spellcasters or invis carries (such as Slark).
Crimson Guard is really good, giving you and your friends that extra survivability. Pipe of Insight is pretty much the same.
Mekansm is okayy, but I think it's wasted on Undying. You've got Soul Rip for heals, and better items to get.
Glimmer Cape and Force Staff are good utility items if you're behind.
If you're winning lots of teamfights, Shiva's Guard is a nice int item to grab.
Ghost Scepter is another great item to get if you're losing and the enemy is mostly physical damage, alternative to Blademail.
I stand by this skill build in every game, for any situation. Undying's ult is amazing, but upgrading it doesn't do much. Soul Rip becomes a powerful nuke+heal very quickly, but you won't have the mana or levels to make it useful too early. Some may argue that maxing Decay so late while still getting aghs is stupid, but don't listen to them. It just works. Trust.
Flesh Golem is so powerful, and the magic amp is often overlooked. When an enemy dies near you it heals you a little, but don't rely on this -- it's more just a sustain thing.
The Tombstone is your multi-purpose enemy-dominator. It's important to know where to place it, and when. After 10 seconds under the tomb, any enemy is screwed, and they know this. Therefore, when you place tomb, you create a choice for the enemy -- fight you, fight the tomb, or run away. If they take too long to choose (or choose wrong), you win.
There are 3 types of tomb positions:
Aggressive -- an aggressive tomb is placed near the enemy, usually blocking their escape or in the middle of a fight. An aggressive tombstone will win your fight if you defend it, or use the distraction to kill the enemy. Drop an aggressive tombatone if you have initiated on a stunned enemy, in a teamfight, or trying to push.
Tactical -- a tactical tomb is placed near the fight but out of the way (for example, on a cliff, or blocking another path). Tactical tombstones are useful if you want to disengage safely, the enemy could quickly kill an aggressive tombstone, or you think there will be an extended fight in a single area (eg rosh pit).
Defensive -- obviously a tombstone placed to cover your retreat, generally as a distraction.
Decay is one of the strongest abilities in the game (probably). It allows Undying to become stronger and stronger as the fight goes on, while weakening the enemy. With Aghanim's Scepter, Undying should have over 3000 health in every long fight -- without any actual strength or health items. However, relying on stolen strength for tankiness means that if Undying is targetted eaely, he'll be nearly useless in fights. Mid-late game, it's important to stay on the edge of fights until you have more health than the enemy. This is very important.
You are only effective when you have more health than the enemy. Decay will quickly tip the scales, but if you go in too quickly, you aill probably die.
Pushing with Undying is pathetically easy.
For lowground towers, stay back, try to build stacks of decay, and when the time comes, drop an aggressive tombstone near the tower, or in the centre of the enemy.
For highground, I like to put the tomb in the enemy base, somewhere past the tier 3 tower. The enemy is forced to target the Tombstone, so your team can attack the tower. While this happens, Decay the enemy, and if you can, Soul Rip the tomb. The tomb usually falls, true, but by the time it does your team should have the tower, or the enemy team should be weakened enough to defeat in a fight.
Okay, so if all goes to plan, you ahould be winning teamfights. Push towers with your team, do as much fighting as possible. Undying is one of the slowest farmers in game, so unless there's an open lane, you really need kills to advance in the game.
You should win fights as 4, so your carry will be able to farm with a lot of space. Focus on towers, be as aggressive as you can. Undying is a pretty mediocre ganker, and an even worse initiator, but he shines in sieges. The more towers and map control your team has, the better.
If you start losing fights, or your team are farming cowards, it's important to know how to back off. Sometimes pushing is the right play, but if your friends do not agree, don't try to prove them wrong by yourself. Undying can literally only teamfight, so despite your raw power, you need your friends. Back off, maybe try to kill a neutral creep (hah, good luck), or something. You can seriously just sit around and watch your carries farm sometimes, it's better than feeding. One day, someone will push, and your time will come again.
I'll probably keep doing things on this, polish it up, etc. Wrote this on my tablet. Don't forget to comment with how much you loved this guide.