Go to Tools menu, Customize Forms, choose the form you wish to share and send it by email using the action button (top right). The recipient just needs to tap and hold on the email .tff file and open in it in Tap Forms. It will not show up on the menu until you then hit the + button and add record to it.
Did the file that you tried to email end with a .tff file extension? Tap Forms will generate a file such as “My Movie Library.tff” which when opened from Mail on another device that has Tap Forms installed will launch Tap Forms and import the form. Then as Roo explained, you just have to tap the + button in Tap Forms, select your form and start adding records to it.