Wi-Fi (other method): CERN has an academic Eduroam network. Eduroam is also available at the Geneva airport.
Mobile network: Lithuanian phones will typically connect to Swisscom (within CERN Meyrin site), which is a Swiss network - expensive, but you can manually connect to (for example) Orange F, which is a French network and therefore EU tariff apply (however, Orange F mobile internet might be slow).
Public transport: www.tpg.ch (get travel times and suggestions https://www.tpg.ch/fr/itineraires unfortunately in French). Getting to/from the airport: Airport (buses 23, 28, 57) <-> Blandonnet (trams run on top of a bridge) <-> CERN (tram 18)
CERN map: https://maps.web.cern.ch
CERN hostel check in (Building 39): on map