This magic skill can be easily increased by spamming the water breathing spell. Find a body of water and jump into it. Keep casting the water breathing spell over and over as fast as possible, you should be able to gain a large amount of skill points in your alteration magic skill tree from spamming this spell.
There is a spell called “Transmute” that can help you increase your alteration magic skill while also earning you a shit ton of money. This spell turns iron into silver and if you cast it on silver, will turn it into gold. As you can guess, selling gold will earn you a pretty penny in the store. This is probably one of the best things to do early in the game. I didn’t do this too much as I needed the iron to raise my smithing, so it was a difficult one to balance out, but this is still a useful one to know if you have a lot of spare iron.