
VF PAGE
<apex:inputField label="Fahrer" value="{!res.Fahrer__c}" >
<apex:actionSupport action="{!LoadingUserDetails}" rerender="out" />
</apex:inputField>
<apex:inputField label="Contact Nummer" value="{!currentuser.phone}" rendered="true" id="out" />
Class
public class CarSharingClass {
public string UserName = UserInfo.getUserId() ;
public Reservation__c res{get; set;}
public user currentuser{get;set;}
public CarSharingClass (ApexPages.StandardController stdController) {
res.Fahrer__c = UserName;
currentuser=[Select Id,phone from User where Id=:res.Fahrer__c limit 1];
system.debug('currentuser:'+currentuser);
res.Contact_Number__c = currentuser.phone ;
}
public void LoadingUserDetails(){
currentuser=[Select Id,phone from User where Id=:res.Fahrer__c limit 1];
system.debug('changeduser:'+currentuser);
res.Contact_Number__c = currentuser.phone ;
}
}

I got to know that action support doesnt work well with look up fields. I found a work around which involves to create a button and call the same method to retrieve values.