You should be able to grind your level up to 2 pretty easily just by hacking enemy portals for 100 AP each time, which is tedious, but past that you're going to have trouble and get bored with 100 AP at a time. Here's a list of things that earn AP - I know most of it is impossible to do at low levels.
You're really not going to be able to do much solo at low levels, so the best option I can think of when you're starting out low level and at a team disadvantage in your area is to organize your local faction and destroy enemy portals in groups. Get at least a couple other people together and attack an enemy portal that is well linked (you'll get more AP for destroying links and fields), low energy and in a location that will allow you to link to the few portals you do control (you get even more AP for creating links and fields than destroying them). It might be hard to find the combo of the those, so take what you can get, but work together.
If you can't find people local at a higher level to help, you might try asking high level players from neighboring towns. Some people are pretty into this game and will take long field trips to help take over outlying regions.
If your opposition isn't very active, you can let your portals decay so that your links and fields disappear, and then relink for a bunch of points.
Finally, a couple options that requires vigilance:
Submit portal suggestions and check to see if they or other portals in your area get added, then be the first to them when they do. You'll need to check http://www.ingress.com/intel and zoom in until it says "Showing all Portals" to be able to see the new portals when they're added.
Another option is to watch your email like a hawk for portal destruction notifications when the enemy destroy a few of your resonators on the few fields you do control, then as with the decaying strategy mentioned before, swoop in and recharge, redeploy and relink your portals. You can do the recharging from a distance if you have the portal key, which will buy you some time to get there to redeploy and relink. I find it helps to leave one low level resonator in an easy to destroy location (like on the sidewalk), and try to place a least one higher level resonator in a hard destroy location (like inside a building). Then you should get notified of the lower level resonator getting destroyed hopefully before they can get to the higher level one.