The value for your apexPageBlockTable tag should reference the list of employees, empList, in your controller. Your add method looks good,but your save method should do an upsert on the employee list, instead of on a single employee. Then, if you add a rerender to the add button on the visualforce page, it can rerender the table when you add an employee, so that it shows the newest list. You'll probably want a rerender attribute on the save button as well. I'm not sure if this is exactly what you're looking for, but hopefully this will set you on the right track.

<apex:page standardController="Employee__c" extensions="recordExt">
  <apex:form>

    <apex:pageBlock title="Employee Records">
    <apex:messages/>
  
    <apex:pageBlockButtons>
    <apex:commandButton value="Save" action="{!mySave}" rerender="employeeSection"/>
    <apex:commandButton value="Cancel"/>
    </apex:pageBlockButtons>
  
    <apex:pageBlockSection id="employeeSection">
    <apex:pageBlockTable value="{!empList}" var="e" >
      <apex:column headerValue="Employee Name">
        <apex:inputField value="{!e.Name}"/>
      </apex:column>
    
      <apex:column headerValue="Last Name">
        <apex:inputField value="{!e.Last_Name__c}"/>
      </apex:column>
    
      <apex:column headerValue="Joining Date">
        <apex:inputField value="{!e.Join_Date__c}"/>
      </apex:column>
    
      <apex:column headerValue="City">
        <apex:inputField value="{!e.City__c}"/>
      </apex:column>
  
      <apex:column headerValue="Phone">
        <apex:inputField value="{!e.phone__c}"/>
      </apex:column>
  
      <apex:column>
        <apex:commandButton value="+" action="{!add}" rerender="employeeSection"/>
      </apex:column>
    
    </apex:pageBlockTable>
    </apex:pageBlockSection>
    </apex:pageBlock>
  </apex:form>
</apex:page>


public class recordExt {

    public Employee__c emp {get; set;}
    public List<Employee__c> empList {get; set;}
    public static Integer addCount {get; set;}
  
    public recordExt(ApexPages.StandardController controller) {
    this.emp = (Employee__c)Controller.getRecord();
    empList = new List<employee__c>();
    }
   
    public void add() {
       empList.add(new employee__c());
      //this.empList = new List<employee__c>();
     }
   
    public pageReference mySave() {
    try{
        upsert empList;
        }
    catch(Exception ex){
            ApexPages.addmessages(ex);
        }
        return null;
   }
  
}