How to pass Lookup field input value from VF page to controller to be passed to another page in Salesforce?

I have a requirement to use contact to create a new case. I have created a new page using case.contactID input field. On pressing a command button, the contact selected should be passed to new VF page so that that can be used to create a New case. But I am currently stuck passing the selected value even to the controller(Null is passed). I am new to VF and Apex. Please advise how to do it, then I will need to pass the value to anther page. Below are my Apex class And VF code.

VF Page Code:

--> -->

</apex:pageBlockSection>
<apex:commandButton value=" Add New Contact " action="{!callcasetabnewcon}"/>
</apex:pageBlock>
</apex:form>
Controller Code: public class Create_case { public case c {get;set;} public id conselected {get;set;} public contact con{get;set;} public string conId {get;set;}

public Create_case () {
case c= new case();
}

public PageReference callcasetabsearch() {
system.debug('Button method called');
Id conID= conselected;
contact con= new contact();
if(conID!= null) {
con=[Select firstname from contact where id=:conID];
}
system.debug('value of contact id is:'+ conID);
//if(c.ContactId != null) {

//con=[Select firstname from contact where id=:c.ContactId];
//strText= con.firstname;
//pageReference pr = Page.assign_1_Case_search;
// pr.getParameters().put('str', strText);
//pr.getParameters().put('msg','success');
//pr.setRedirect(false);
//return pr;
//}
//else
return null;

}