There are various different ways you can populate the value of a field using post data. Here are some of the most common methods:
Post Management Add-On
The value of a field can be populated using the Post Management add-on. Learn more.
#post_meta
The #post_meta variable can be used to extract meta data from the post you form is placed on.
For example, putting #post_meta("my_meta_key") in the default value of the field would pre-populate it with the meta value of the meta key my_meta_key.
PHP
The value of a field can be populated using WordPress filter hooks and PHP. Learn more.