Question
Salam alaykun,
 When an alif that usually begins an ayat does not have a vowel [fatha,domma or kasra] how do we determine the vowel to assigned to the word?

Answer
Wa alaikum assalaam wa rahmatullahi wa barakatuh,
The question is referring to hamzah Al-Wasl.  This is a hamzah that is not used when continuing reading, but employed only when started the word. 
There are several lesssons on the site explaining how to determine the vowel that we should used when starting a word that begins with hamzah al-wasl.  Please see:
http://www.abouttajweed.com/hamzah-al-wasl/index.php

Also, for a list of words that start with hamzah al-wasl after a marked stop in the Medina Complex printing of the Qur'an, and the proper vowel to start on, please see:
http://www.abouttajweed.com/downloads/useful-documents/verbs-and-nouns-beginning-with-hamzah-al-wasl/download.html