Juking is the best skill in the game along with going on killing rampages. Staying alive becomes just as important as being the ultimate killer in a game. The less you die, the less experience and gold the enemy team gets. Those who fail at this skill are called feeders (giving your opponent constant kills, which causes him to level up) and are looked down at in every game. Staying alive isn't an exact art and can be achieved in multiple ways such as through items, juking, skills, or just some other godly hypnosis.
Juking
Firstly, the art of juking is one we all learn over time because of experience in maps and heroes. The art of juking is, in other words, making an unexpected turn or move that causes your enemy to lose track of you. Line of Sight is the basic factor in it and must be paid close attention to. Your goal is to stay out of his Line of Sight (LoS). It gives you time to find a way out or just port back to base. Rather than just running around like a chicken with its head cut off, try to think of places to hide. Most new players make the mistake of doing the former of the two choices.
Fact: Every year 643,975 tigers die of exhaustion while trying to catch chickens.The juke will allow you to build enough mana for a stealth, stun (very effective to run away), or to activate boots to book it. Just executing a single juke won't put you in the clear, you need to play around the map a bit so the opponent completely loses you. Try to first juke him and then continue going around places he wouldn't expect you to run. Go around to his jungle or cut back to where you just ran from. The possibilities are all dependent of the player's imagination. The opponent's reaction will be something of this sort...
Where did he go?!Hopefully you'll get away from the opponent then, but if you don't, there are a few more ways of getting away which are all about getting out of his Line of Sight. If he can't constantly see you, then he can't stun or hit you. Try running around an area for a few rounds then pull back right through him. He'll follow you around for a bit then, before he can figure out that he should double back you'll be out of there. However, if all else fails, use the most efficient method ever invented. The one and only Homecoming Stone, something that will save your life so many times you won't believe.
Escaping Mechanisms
Lastly, you have the normal abilities to run away. Heroes such as Nighthound are the kings of escaping. Nighthound itself has a constant stealth as its ultimate ability. That is a skill that will be the constant bane of the enemy. You can pop away and come back for a kill any time. Others like Andromeda or Pestilence can just stun and run. You turn around for a second for the stun, then use boots or just run and use juking. They will quit on you most of the time but it's best to be safe.

Apart from the abilities, you also have the multiple items that make staying alive easier. Items such as Assassin's Shroud (ineffective with Pestilence), Homecoming Stone and boots are the godsends of escapees. The Assassin's Shroud allows you to go invisible for a certain amount of time and run like all hell is loose behind you. The boots allow you to go at superhuman speed in the opposite direction of your hunter, and the Homecoming Stone is the king of all escape weapons. Use the stone to pop back to a tower or base and heal up for another day if you notice that the opponents are too formidable or outnumber you. Portal Key is also one of the best escape mechanism, but it can also be used to save a whole team if a hero carrying it has a stun. A good Magmus or Witch Slayer will be able to stun three or more enemies to allow his ally to escape, and can often use his Portal Key to save himself just after the stun.
The Rest...
Staying alive is very dependent on the concepts mentioned above but also most dependent on preventing it in the first place. All you have to do is be aware of the map. The heroes can never have a chance at taking you down if you make sure to move back as soon as they come too close to gank. Another concept is "tower hugging." If you see that a strong contingent of heroes and creeps are advancing on a tower, instead of meeting them out there where they can stun and destroy you, you stay back and stay in tower range to stay alive and be able to slow the opponent. It saves you from giving a free kill, while allowing reinforcements to arrive. Also, heroes with blink abilities should
always blink out of the fights rather than in.