You could do it that way
<select name="foo[]" multiple="multiple">
<option value="dog">Dog</option>
<option value="cat">Cat</option>
<option value="fish">Fish</option>
</select>
<?php
$pets = $_POST['foo'];
$query = mysql_query("INSERT INTO `pets` (`pet1`, `pet2`, `pet3`) VALUES ('".$pets[0]."', '".$pets[1]."', '".$pets[2]."')");
?>
But honestly, this is a terrible way to build a database. It will be very unpleasant or difficult to do something meaningful.
Why not create the following database setup:
users:
id | name
----------
1 | Tim
Pets:
id | user_id | type
-------------------
1 | 1 | Fish
2 | 1 | Cat
3 | 4 | Kakapo
, .