What's the fastest way to level up to level 2 in ingress?

Hack plenty of enemy portals. You get 100 AP for hacking an enemy portal, but none for hacking a friendly one.

If there are no unclaimed portals around (highly likely in some locations), find a level 1 enemy portal and start slugging away. You'll want a few dozen XMP bursters at minimum to destroy the portal, but the rewards are high--destroying 8 resonators and planting 8 of your own on a single portal will get you almost a quarter of the way there. Even if you don't manage to capture the whole portal, you'll still have gotten 75 AP for each resonator you destroy.

Deploying portal shields is a good way to get AP that may not be obvious at first. Check every friendly portal you encounter to see if it has a full complement of shields. If it doesn't, deploy as many as you can. You get 150 AP for each one.

Creating links and fields generates the most AP at that stage.

http://ingressportal.com/research/experience-ap/

Finding neutral portals and filling them with resonators is probably the fastest way of gaining AP.

Each portal you build up with 8 resonators and 4 shields will reward you 2000AP. Do this 5 times and you are level 2 :-)

Avoid to recharge lonely portals (recharging a portal will give you 10AP per charge), sometimes it is better to let them decay to neutral and then rebuild them, more AP at the end.