I am stuck at level 1 with 3000/3000 XM.
I can see XM but I can't collect it anymore. Is there anything mandatory to be able to level up?
In order to level up you need to gather AP not XM (XM is energy, AP - experience), you should see an octagonal progress bar in the upper left corner.
In order to get AP you need to deploy resonators, blow up enemy resonators, build links, etc. Here are the exact numbers for each action:
Placing a resonator 125 AP
Destroying a resonator 75 AP
Placing the first resonator on a portal 500 AP
Placing the eighth resonator on a portal 250 AP
Updating another agents resonator 65 AP
Updating your own resonator 0 AP
LINKS:
Creating a link 313 AP
Destroying a link 187 AP
FIELDS:
Creating a control field 1250 AP
Destroying a control field 750 AP
OTHER:
Applying a portal shield 150 AP
Hacking an enemy portal 100 AP
Recharging a portal 10 AP
To look for portal in your area use http://ingress.com/intel
As already mentioned you need to get AP, not XM to level up.
For a great list of point values associated with actions and other useful info, check out the Ingress Field Guide.
How you go about getting AP will depend on the situation for your side in your area, but here's a few general guidelines for getting past the early levels:
I agree with other answers. They just forget to mention Glyphing. If you hold hack button for 3 seconds the series of one to four signs shows up. If you repeat them (or just part) you will get bonus items, more AP, and you will get AP even from friendly portals.
There are lot of guides to check for more tips.