first, check out the "handling file uploads" section in the php manual ...
http://www.php.net/manual/en/features.file-upload.php
then, I would recommend the following:
in your dogs table, add a field "picture" (datatype text).
on upload, give the uploaded picture a filename consisting of the dog's record id, maybe: dog_28803.jpg, and store it in a pics directory. write this filename into the record's picture field, too.
if you show the dog info, get it from the database and, if given, write an image tag, eg:
if($thedog['picture'] != '')
echo "<img src=pics/".$thedog['picture']>";
a note:
basically you don't need to store the filename in the table because it can be constructed by the record id. but I prefer this way because it's future-proof (you might want to link external pictures as well, some time).
HTH!