Leveling in Ingress is pretty straightforward.
For each level you have to achieve a certain amount of action points. As you level up you can use higher level items. The max level of items you can use directly correlates to the level you are.
In order to obtain action points in the game you have to complete certain actions. You gain more points by building up portals and fields than by destroying them but it takes more time and effort to build up fields than it does to tear them down normally.
As you can see in the chart below creating a control field by far and away the best place to gain action points and level up. However, it is also the hardest to do because at low levels portals have to be in close proximity to each other fully charged portals and that can take some time. In addition the acquiring of the portals keys required to link all the portals together can also be time consuming.
|Action||Action Points Earned|
|Place a resonator||125 AP|
|Place the first resonator on a portal||500 AP|
|Place the eighth resonator on a portal||250 AP|
|Create a link||313 AP|
|Create a control field||1250 AP|
|Upgrade a resonator||65 AP|
|Recharge Resonator(s)||10 AP|
|Hack an enemy portal||100 AP|
|Destroy a resonator||75 AP|
|Destroy a link||187 AP|
|Destroy a control field||750 AP|
You can also enter in passcodes to gain action points but they are in small amounts (10-200 APs generally) that it is a hard way to actively level up.
Here is how many action points it takes for each level as well as some basic stats.
|Level||AP required||Max XM||Best (solo) Portal|