How to get a form field to allow additional values?
If you want to allow a field to get multiple values.you need to edit the field and allow the numbers of values to unlimited.
Suppose you want to allow multiple images to upload in Article content type.

1)Go to Administration » Structure » Content types » Article » Manage fields 
2)Edit the field and under field settings,choose the values to unlimited or number of values you want a user can upload.
See the similar in screenshot url below.
https://www.evernote.com/shard/s496/sh/15655bf1-104c-40ed-ab26-bc6da6ebe7a5/bd1bce151edec9956746845474f3ba95