What is the most effective way to help a friend leveling up?

Since you are level 60, you should have more currency than your friend. Enough to buy some leveling uniques that would make his journey through earlier levels a breeze.

• dual Perandus Signet, worth 45 chaos in Prophecy at the moment, with 2% increased Experience gained
• a Tabula Rasa, around 10 chaos, so that he wouldn't worry about linking sockets in the beginning of his game

Other leveling gear will depend on what build your friend is going to roll:

Casters

• Lifesprig, worth 1 chaos
• Reverberation Rod from level 24, worth less than 1 chaos
• Wanderlust gives a nice movespeed bonus for casters early in the game, for 1 chaos
• Atziri's Foible (1 alch, usable from level 16) makes you forget your mana problems.
• Sidhebreath for Necromancers-to-be, worth 1 alch.

Trapper

• Deerstalker from level 22, worth 1 alch
• Sunblast from level 37, worth 1 alch

Bow

• Storm Cloud from level 9, worth 1 chaos
• Quill Rain from level 5, worth 1 chaos
• Briskwrap from level 9 or Foxshade later, from level 25, both less than an alch.
• Hyrri's Bite from level 10, worth around an alch.
• Goldrim early on, worth 1 chaos.

Melee

• Wideswing for insane AoE on melee skills from level 18, worth less than an alch
• Facebreaker on from level 16 for crit melee, worth 1 chaos
• Meginord's Girdle from level 8, worth 1 chaos
• Blackheart, worth 2 chaos, with a potential to turn into overpowered Voidheart if you friend likes the game enough.
• Wurm's Molt from level 8 for life leech, worth 1 alch
• Limbsplit from level 13, worth 1 chaos
• Kaom's Sign, worth 1 chaos each, especially if you are going Endurance charges

Totems

• Night's Hold from level 10, worth around 10 chaos in Standard, but extremely useful for leveling with Flame Totem early.

On top of that, do not underestimate the complexity of this game. Play along with your friend and be there to answer his questions.

You can try, but he has to like the "grind" on his own. The best things you can do if you want to "rush":

• Buy him leveling uniques (advise in other answers / forums / guides)
• Get him waypoints across areas for faster progression
• Advise on actual leveling / farming areas (dried lake, ledge etc)

Overall if he's new, just make a fresh char and play along, or let him come along slowly. There's a lot of complexity and depth in poe, which you only uncover if you grind... He has to like the repetitive grinding, item discovery etc. on it's own (else he'll never get into poe) so rushing a new guy may not be a good idea anyways.

You have to have the excitement of seeing a unique drop and then iding it and reading about it (then discovering that it's junk, repeat 1000 times) and be willing to continue on if you're going to get into poe.

Another option for powerleveling has been recently discussed on Reddit.

The higher-level character wears Southbound. Unless his damage has cold or damage over time components, his hits will leave the mobs at 1 hp. The lower-level character follows in his path, far enough not to trigger the experience penalty. To be fast, the lower-level character equips an area of effect skill and / or Increased Area of Effect support gem. Quicksilver flasks and Seven-League Step are recommended.