Go on quests and kill every enemy with destruction preferably a high level, expert etc, also using healing hands and flames on a horse is a good way to increase restoration and destruction at the same time

Just use the oghma infinium glitch

What I did was I used the Fireball spell non stop on every enemy I faced. I also carried a lot of Health and Magicka potions on me so I wouldn't die.

Using the Oghma Infinium glitch is a quick way to level all of your skills. However that would require you to delete some patches and to the glitch, and it cannot be done if you have already read the book. Another thing to note is that Destruction levels faster if you use a strong spell. Constantly casting stronger spells will level it quickly, but there is no way to efficiently level it unless you use a unkillable enemy such as Shadowmere.

If you are relatively new to Skyrim and don't know the benefits of any of the standing stones, I would choose the one you like the most, then go to Riverwood (If you chose to go with Ralof at the intro of Skyrim) and sleep at Gerdurs house so you can get the 'Rested' or 'Well Rested' bonus. These bonuses either will give you 10% more experience or a 5% experience. Just remember the Lovers Stone overrides the effects so choose which you would prefer wisely.



Okay so since I don't really want to make a topic out of this I going to end it here. But could probably look up on Google or something for more suggestions. Have a good day.