There isn't a lot of information online about this, and what information there is seems mostly outdated.
FWIW, I went to the Al Dur Jetty (aka Ad Dur) as one site (from the Bahraini government - http://www.mofa.gov.bh/Default.aspx?tabid=134) said the boat left daily from there at 10am.
The guard at the Jetty told me to go to Durrat Al Bahrain instead (quite a way further south).
When I called the hotel on the islands (https://www.facebook.com/Hawarislands/), at +97317641666 the lady told me that for day trips the only option is to go on Friday at 8am and return at 3pm.
Otherwise you must stay overnight and leave at 2pm and return at 3pm the next day.
She said the only other way is if you have your own boat; there seem to be companies offering tours there but information is a bit skimpy there too so YMMV.