These methods are both long BUT WILL SAVE YOU HOURS OF WORK. Read carefully and try it out.

Score Multiplier 4 times: Zoltun Kulle
I haven't seen this method in the internet yet, so here it goes. (A friend showed me this method btw.)
Starting off, you must have at least 2 PLAYERS to do this. 1 will have the normal score, the other will have his score multiplied 4 TIMES.
(You is the player who gets the score of 4 times)
1. Both players go to Zoltun Kulle, Kill him, and before any of you go get the black soul stone, the person who wants the score of 4 times leaves the game. The person who is still in the game, don't get the soul stone, just chill.
2. The person who has left the game, start a new game, and get the black soul stone (using teleport), then talk to Adria, get the xp, leave the game.
3. Join your friends game, and you should have the objective as get the black soul stone again. Ask your friend to take the black soul stone, then he leaves the game. You talk to adria. Get xp. Leave game.
4. Join your friend's game. Ask you friend to leave. Talk to Adria,get xp, and leave the game.
5. Join your friend's game, ask him to talk to Adria. You both get XP. Boom. 4 times the xp for you.
We used to be able to do the infinite method where we repeated step 4 again and again but unfortunately, it has been nerfed, so this is the best one available.
If you have the error - host has left the game, you haven't done it right, unless some time from now, it has been nerfed. This method is great for quick but boring leveling.

Quick and fun leveling
Again, you will need two people for this for maximum speed. You can do this alone, but i think getting a very high leveled person to help you do this will make time fly by. Also an extremely simple method. (You can get quite a lot of money from doing this as well.)
(You is the person getting power-leveled)
1. I'll assume you've made a new class and you're in normal mode. Firstly, start your journey yourself. Complete the first mission. Then call you friend up to help you.
2. Ask him to go the final mission and objective of act 1 in normal. There should be a man saying that he will be taking you to Caldeum. Once you're there in Caldeum, both of you leave the game.
(In the beginning, I seriously recommend that you use the method above. Once you reach level 15, continue to step 3. - not vitally important, but highly recommended)
3. Ask your friend to take you to Belial. Let him kill Beilial for you. Run around like a mad chicken, seriously, you'll get one hit killed. If you die, ask him to bring you back. No xp earned if you're dead remember!
4. Once Beilial is dead, this is where the true power leveling starts!
5. Ask your friend to take you to the final mission of act 3. DON'T KILL AZMODAN, instead, got to all Arreat Crater levels. Ask your friend to kill all the monsters for you. Run like a mad chicken again. When masses of those scorpion monsters come out, seriously stand back! You can get loads of xp from those guys! When you see a cave door leading to another room, teleport back to base and teleport to another Arreat Crater level.
(Remember to go to the Auction house and get XP bonus and multiplier items after every 5 levels or so. Saved me almost 5 hours worth of work.)
6. Once all Arreat Crater levels are done, go to the bridge of Korsikk and Rakkis Crossing and kill all the monsters there until you see the door leading somewhere else.
7. Then go to the dungeons right next to the base in Act 3. Kill all the monsters there.
8. Once all of that is done, both of you leave the game, make a new game, and do it again!
9. Once you reach level 30-35 (doesn't matter which one), kill Azmodan and then Diablo.
10. Repeat all steps other than 9 and do it in nightmare until level 45-50, kill Azmodan and then Diablo.
11. Then repeat all steps again other than 9 and 10 until level 60.
This method takes 20 hours, which is a lot. But playing without this method is almost or even more than double the time!
If this helped you, please say so. Trying to become an official Clraik. Thanks.