What to do if APN settings appear disabled
Sometimes, APN settings on your device for a particular carrier may be "locked" such that they are "grayed out" and can't be modified. While this is often an indication that you shouldn't need to modify them, it's sometimes possible to work around this.
Reset to default option
At the APNs screen, try the Reset to default option available by pressing the overflow menu button. This will delete any of your customizations to APN settings and return them to their initial state as provided by the manufacturer. Often this will result in the settings no longer being disabled.
Airplane mode option
You may also try removing the SIM card and/or entering Airplane mode (called "Flight mode" on some devices) prior to selecting the Reset to default option.
Note that your device may need to be rebooted after removing the SIM card. After this, try the Reset to default option and/or set up the APN configuration that you want.
If you removed the SIM card, replacing it may require another reboot.