There's a lot of information about creating a form in Acrobat's help doc and in a number of tutorials here.
In order for Reader users to save a filled-in form, it has to be Reader-enabled, which you do by selecting: File > Save As > Reader Extended PDF > Enable Additional Features
In order for Reader users to save a filled-in form, it has to be Reader-enabled, which you do by selecting: File > Save As > Reader Extended PDF > Enable Additional Features