Visualforce Page for customizing Attachments. See UploadAttachmentController.

UploadAttachment

<apex:page standardController="Contact" tabStyle="Contact" extensions="UploadAttachmentController">

 <apex:sectionHeader title="{!Contact.Name}" subtitle="Attach File"/>
 
 <apex:form id="form_Upload">
 <apex:pageBlock >

 <apex:pageBlockButtons >
   <apex:commandButton action="{!back}" value="Back to {!Contact.Name}"/>
   <apex:commandButton action="{!back}" value="Cancel"/>
 </apex:pageBlockButtons>
 <apex:pageMessages />
 
  <apex:pageBlockSection columns="1">
  
    <apex:pageBlockSectionItem >
      <apex:outputLabel value="File" for="file_File"/>
      <apex:inputFile id="file_File" value="{!fileBody}" filename="{!fileName}"/>
    </apex:pageBlockSectionItem>
  
    <apex:pageBlockSectionItem >
      <apex:outputLabel value="Type" for="type"/>
      <apex:selectList value="{!selectedType}" size="1" id="type"> 
        <apex:selectOption itemValue="Plain ole awesome" itemLabel="Plain ole awesome"/>
        <apex:selectOption itemValue="Super awesome" itemLabel="Super awesome"/>
        <apex:selectOption itemValue="Most awesomest" itemLabel="Most awesomest"/>
      </apex:selectList>
    </apex:pageBlockSectionItem>
    
    <apex:pageBlockSectionItem >
      <apex:outputLabel value="Is the file awesome?" for="visible"/>
      <apex:selectList value="{!selectedAwesomeness}" size="1" id="visible">
        <apex:selectOption itemValue="false" itemLabel="No"/>
        <apex:selectOption itemValue="true" itemLabel="Yes"/>       
      </apex:selectList>
    </apex:pageBlockSectionItem>    
    
    <apex:pageBlockSectionItem >
      <apex:outputLabel value="Description" for="description"/> 
      <apex:inputTextarea id="description" value="{!description}" rows="4" cols="50"/>
    </apex:pageBlockSectionItem>
    
    <apex:pageBlockSectionItem >
      <apex:outputLabel value="" for="uploadBtn"/> 
      <apex:commandButton id="uploadBtn" value="Attach File" action="{!processUpload}" />
    </apex:pageBlockSectionItem>    
    
  </apex:pageBlockSection>
 
 </apex:pageBlock>


 </apex:form>

</apex:page>

UploadAttachmentController

public class UploadAttachmentController {
    
    public String selectedType {get;set;}
    public Boolean selectedAwesomeness {get;set;}
    public String description {get;set;}
    private Contact contact {get;set;} 
    public String fileName {get;set;}
    public Blob fileBody {get;set;}
    
    public UploadAttachmentController(ApexPages.StandardController controller) { 
        this.contact = (Contact)controller.getRecord();
    }   
    
    // creates a new Contact_Attachment__c record
    private Database.SaveResult saveCustomAttachment() {
        Contact_Attachment__c obj = new Contact_Attachment__c();
        obj.contact__c = contact.Id; 
        obj.description__c = description;
        obj.type__c = selectedType;
        obj.awesome__c = selectedAwesomeness;
        // fill out cust obj fields
        return Database.insert(obj);
    }
    
    // create an actual Attachment record with the Contact_Attachment__c as parent
    private Database.SaveResult saveStandardAttachment(Id parentId) {
        Database.SaveResult result;
        
        Attachment attachment = new Attachment();
        attachment.body = this.fileBody;
        attachment.name = this.fileName;
        attachment.parentId = parentId;
        // inser the attahcment
        result = Database.insert(attachment);
        // reset the file for the view state
        fileBody = Blob.valueOf(' ');
        return result;
    }
    
    /**
    * Upload process is:
    *  1. Insert new Contact_Attachment__c record
    *  2. Insert new Attachment with the new Contact_Attachment__c record as parent
    *  3. Update the Contact_Attachment__c record with the ID of the new Attachment
    **/
    public PageReference processUpload() {
        try {
            Database.SaveResult customAttachmentResult = saveCustomAttachment();
        
            if (customAttachmentResult == null || !customAttachmentResult.isSuccess()) {
                ApexPages.AddMessage(new ApexPages.Message(ApexPages.Severity.ERROR, 
                  'Could not save attachment.'));
                return null;
            }
        
            Database.SaveResult attachmentResult = saveStandardAttachment(customAttachmentResult.getId());
        
            if (attachmentResult == null || !attachmentResult.isSuccess()) {
                ApexPages.AddMessage(new ApexPages.Message(ApexPages.Severity.ERROR, 
                  'Could not save attachment.'));            
                return null;
            } else {
                // update the custom attachment record with some attachment info
                Contact_Attachment__c customAttachment = [select id from Contact_Attachment__c where id = :customAttachmentResult.getId()];
                customAttachment.name = this.fileName;
                customAttachment.Attachment__c = attachmentResult.getId();
                update customAttachment;
            }
        
        } catch (Exception e) {
            ApexPages.AddMessages(e);
            return null;
        }
        
        return new PageReference('/'+contact.Id);
    }
    
    public PageReference back() {
        return new PageReference('/'+contact.Id);
    }     

}

Hi Jeff,
Thank you. Got error: Required fields are missing: [File Name, Body] while trying to add an attachment. (But the record is added, when I go to the Account file. And when I view the file attachment (view link) its empty)