[SalesForce] Attach dynamically generated visual force PDF to a visual force template

Assuming "Project" is a custom object.

Enable notes and attachment for the custom object.

When you click 'generate invoice', just before redirecting to VF page use getContent() method. E.g;

public PageReference generateInvoice()
{
     Attachment att = new Attachment(name ='Invoice_AnyUniqueName.pdf');
     PageReference invoicePage = Page.GeneratingInvoicePage;
     invoicePage .getParameters().put('id',projectRecordId);
     // return page content as blob type
     // Alt: att.body = invoicePage .getContentAsPDF();
     att.body = invoicePage .getContent();
     // Associate with project's record Id
     att.parentid = projectRecordId;
     insert att;
     return invoicePage ;
}

On the attaching the PDF part of your question, you can connect your button to a controller method as described in e.g. Call Apex Class From A Custom Button.

To generate the PDF and attach it you can use the getContentAsPDF method and insert the Attachment:

global class MyClass {
    webservice static void attachPdf(Id customObjectId) {
        PageReference pr = Page.YourPageName;
        // Add parameters (if any) passed from the custom button or queried locally
        pr.getParameters().put('id', ...);
        insert new Attachment(
                ParentId = customObjectId,
                Name = 'Whatever Name You Want',
                Body = pr.getContentAsPDF(),
                ContentType = 'application/pdf'
                );
    }
}