For your mobile data connection (which should work without gapps) make sure you have set the correct APN for your network and provider/carrier.
Usually your provider/carrier should have the settings you need on his website.
Access your APN configuration:
- Tap “more” under the wireless/networks tab in settings
- Tap “mobile networks”
- Tap "access point names"
Then choose your network and tap on an access point to change the config or hit the menu button on the phone (bottom left) to create a new one.
Also be sure you have mobile data as part of your contract.
The solution for your gapps problem is much more trivial:
Find the widget “Google apps installer” in your widget drawer and drag it onto your homescreen.
Then tap it to install gapps.
Edit: more thorough instructions here: