I am going to show you how can you train your Alteration skill to level 100. But first I am going to show you something else. If you finished the suggested quest from Part 11, you should receive this letter. I suggest to do this quest too. Your reward is a shield. If you would like to buy a house in the city speak to the Jarl, she has a small task for you.
If you disenchant the shield you will get an another and better Resist Magic enchantment. To train the Alteration skill you need the Detect Life spell. You can easily get it by this quest. The Mage Stone. Travel to a well populated city.
Equip the gear from Part 8. Take some rest. Find a place with a lot of people and start casting the Detect Life spell with both hands. At night the inn is a good place or you can wait until morning. I didn't give time to this method because it depends on the population. It took me 22 minutes to reach level 100.
In the next part I am going to show you how can you train the Speech skill to level 100 within 15 minutes.