How do I enable saving of filled-in fields on a PDF form?

Open your PDF in Google Chrome. Edit the PDF as you want. Hit ctrl + p. Save as PDF to your desktop.

When you use Acrobat 8, or 9, select "enable usage rights" from the Advanced menu. This adds about 20 kb to the pdf.

The other possibility is to use CutePDF Pro, add a submit button and have the XFDF data submitted to your self as an email or to a web server. The XFDF data can then reload the original PDF with your data.

You can use the free foxit reader to fill in the forms, and if you pay a little you can design the forms that way you want.

You can also us iText to programmaticly create those forms.

There are free online services that allow you to upload a pdf and you can add fields also.

It depends on how you want to do the designing.

EDIT: If you use foxit reader, you can save any form that is fillable.

If you are using Adobe Acrobat X to make the form, set all the fields as you want them, then click File, Save As, Reader Extended PDF, Enable Additional Features. The resulting PDF form can be saved when filled in, if opened in versions of Adobe Reader before XI.