Dive to find Sayaka's soul gem. Click on Sayaka once to "magnetise" her to the cursor, then move it around and she will follow. The mobile phone signal gives you the gist of how close you are, but it's not very precise. Her portrait also changes to reflect the proximity. When you want to dive and search for it, click once again. The colour of the cross that shows up if you miss is also an indication of your proximity.
You're timed in sped-up days, hours, minutes and seconds. I don't know if it's possible to not get the bad ending (her crying) but I got it in two clicks pretty quickly and still got it.