Adding a new taxonomy term from a custom content type field
Check out taxonomy_save_term(). Here's an example from the comments:

$term = array(
'vid' =&gt; 5, // Voacabulary ID
'name' =&gt; 'Drupal', // Term Name
'synonyms' =&gt; 'Druplet', // (Optional) Synonym of this term
'parent' =&gt; 11, // (Optional) Term ID of a parent term 
'relations' =&gt; array(15), // (Optional) Related Term IDs
);

taxonomy_save_term($term);


You could use this inside hook_nodeapi() on the operations insert or presave (and update). See the comments at the first link for more info.

EDIT: For drupal 7 you have to check out the node api instead of of hook_nodeapi().