Having someone run you through MP10 normal Keeps 2 until level 25 is your best bet to start.
At level 1, equip a Hellfire Ring for the 35% EXP bonus.
At level 14, equip a Leoric's Signet for another 20-30%
At level 23, equip three pieces from the Cain's Fate set. Add a Radiant Star Ruby to the helm (or be baller with a Marquise).
Enter Nightmare and have someone run you through MP10 Nightmare Keeps 2 until level 50.
At level 33, equip Slave Bonds http://us.battle.net/d3/en/item/slave-bonds
for bonus movement speed to keep up with your leveling buddy.
Enter Hell and have someone you run you through level 60, repeating MP10 Keeps 2 as before.
For solo, it takes much longer. You should still equip the bonus EXP gear and MS items as before, but a high DPS weapon is more important to clear MP10. At levels <30, get a weapon with a socket ASAP and throw in a high level ruby.
Between levels 30-42, use Spectrum http://us.battle.net/d3/en/item/spectrum-Fa7AX
It can roll >600 DPS, making it the best early levels twink weapon.
After level 42, you can try getting a reduced level requirement weapon that's higher DPS than Spectrum. High LOH at any point in time is great for survivability.
Get access to Keeps 2 at any difficulty level as soon as you can and just grind until you reach the required levels to unlock new difficulties.