I used Ron's example from the this post to make an editable table that displays related records and it works perfectly! Now, I'm trying to find a way that I can use this same page, but have it add rows to create new records in addition to editing existing records.  

I have an object called time_off_request__c that is the parent of time_off_day__c.  Basically, I want the user to be able to create a new time off request and add as many days as they'd like all on one screen.  

Here is my code-

VF Page

<apex:page standardController="Time_Off_Request__c" extensions="timeoffdayController">
 <style>
.pbBody td {
 border-color: #E3DEB8;
 border-style: none none solid;
 border-width: medium medium 2px;
 padding-bottom: 4px;
 padding-top: 4px;
 width: 85px;
}
.pbBody input   { width: 105px;}
.pbBody .nameColumn { width: 125px;}
.hdr     {;}
</style>
<apex:form >
 <apex:messages />

 <apex:sectionHeader title="Days for" subtitle="{!Time_Off_Request__c.name}" />
 <apex:pageBlock title="Edit Days">
  <apex:pageBlockButtons >
   <apex:commandButton action="{!saveChanges}" value="Save"
    rerender="main" status="ajaxStatus" />
   <apex:commandButton action="{!cancel}" value="Cancel" />
  </apex:pageBlockButtons>
  <apex:actionStatus id="ajaxStatus" startText="Updating time off request...">
   <apex:facet name="stop">
   <apex:outputPanel id="main">
    <table>
    <tr>
     <apex:repeat value="{!headers}" var="h">
      <td class="hdr">{!h}</td>
     </apex:repeat>
    </tr>

    <apex:repeat value="{!Days}" var="a">
     <tr>
      <td><apex:inputField value="{!a.Date__c}" /></td>
      <td><apex:inputField value="{!a.Hours__c}" /></td>
      <td><apex:inputField value="{!a.Note__c}" /></td>
     </tr>
    </apex:repeat>
    </table>
   </apex:outputPanel>
   </apex:facet>
  </apex:actionStatus>
 </apex:pageBlock>
</apex:form>
</apex:page>

Class

public class timeoffdayController {
  
  // Constructor
 public timeoffdayController(ApexPages.StandardController controller) {
  this.request = (Time_off_request__c)controller.getSubject();
  
     this.day = [ SELECT 
      d.SystemModstamp, d.Name, 
      d.LastModifiedDate, d.LastModifiedById, d.LastActivityDate, 
      d.IsDeleted, d.Id, d.Date__c, d.CreatedDate, d.CreatedById, 
      d.Time_off_request__c, d.Hours__c, d.note__c  
   
      FROM 
      Time_off_day__c d 
      WHERE 
      d.time_off_request__c = :request.id ];
 }
 
 // Action Method called from page button
 public pagereference saveChanges() { 
  upsert this.day;
  return null;
 }
 
 // Action Method called from page link
 public pagereference newDeliverable() { 
  time_off_day__c d = new time_off_day__c();
  d.time_off_request__c =this.request.id; 
  day.add( d );
  return null;
 }
 
 // public Getter to provide table headers 
 public string[] getheaders() { return new string [] 
  {'Date','Hours','Note' } ; }
 
 // public Getter to list request days
 public time_off_day__c[] getDays() { 
  return this.day; 
 } 
 
 // class variables
 Time_off_request__c request;
 time_off_day__c[] day; 
}