How to level my merc quickly?
Don't try to level up the mercenary, he will level up in time. Just play the game, sorceress doesn't need a mercenary anyway. Stay away from your foes and keep showering them with the frozen orb, fire wall, or whatever you have in mind
Thanks to @FoxMcCloud for the hint. Apparently there is really no point in leveling your merc, because it will have the same stats as the one you will purchase at a high level. I thought that if you get your merc at level 10 and keep it until a high level, it would be better than a merc that you buy at that same high level.
The confusing statement, that lead me to believe that was from the Diablo Wiki Merc Guide. Here is the part that refers to the stat gain of mercs:
Merc Stats and Leveling Mercs
When you are being shown mercs to hire, the game lists the merc's name and type, along with cost, defense & life.
[...]
At each difficulty level (hence referred to as diff.), the mercs you can hire will be of a higher experience level than those of the previous diff., however their stats will be lower when compared to a merc from the previous diff. who has reached the same level of experience. In short, leveling up your normal diff. merc is better than hiring a new one at a higher difficulty level.
Note: The actual difference in the physical stats of a normal diff. merc and nightmare diff. merc isn't tremendous and there are only a few levels of difference in their skills. To give an example, at level 80, a normal rogue merc has 1290 life and 199 dexterity (dexterity). A nightmare rogue merc would have 1256 and 194 dexterity.
In short, it won't make a tremendous difference to your PvM (player vs. monster) game if you hire a merc in hell diff. Only Act II nightmare diff mercs are really affected by this. If you wish to have those particular auras then you are going to have to settle for slightly lower stats.
So this statement refers to the stat difference between the same mercs from different difficulties (for example Act 2 Desert Warrior Normal vs Hell). Since there is no point in buying mercenaries from Hell, because they have the same abilities like the ones in normal (Desert Warriors), this mechanic of the game is not worthy to ever keep in mind.
I tested this with my level 82 Paladin. He had a merc from Nightmare Act 2, that I bought at around Level 40. I compared this with his replacement from the same Act/Difficulty and they had the same stats (Dex/Str at the same level).
Original Question:
Since we established that there is no point in leveling the merc. The guide linked above still mentions the best situations for leveling him up:
Mercs get the most experience when you are fighting monsters of a similar level to that of the merc. If you've just hired a new merc and want to level them to the same level as your character, compare their level to that of monsters in different parts of the game and fight in that area. You can find the data here . With players 8 active, the merc will level up pretty quickly.
Mercs also get more experience for monsters they kill themselves, rather than the XP they get when your character kills monsters. Assist your merc by lowering monster HP for and backing off, or using spells/skills that effect whole groups of monsters to weaken them and allow your merc to finish them off. Try to pick monsters that are unlikely to hit your merc hard and often, e.g.. Frenzytaurs in the Ancients way. These monsters are very likely to take your merc apart quite quickly. Places like the Arcane Sanctuary, where your merc can take on monsters without being swamped are ideal.