you will need to copy the file app/design/frontend/base/default/template/customer/form/edit.phtml to app/design/frontend/default/default/template/customer/form/edit.phtml then add an input file or else inside it.
Here an example (the code is customized, so adapt to your situation):
<label for="language" class="required"><em>*</em><?php echo Mage::helper( customer )->__( My language ) ?></label>
<div class="input-box">
<input type="text" value="<?php echo $this->getCustomer()->getLanguage(); ?>" id="language" name="language" />
</div>