Paula,
Kent made a good point in suggesting to check out the Bahn train website.
Another way to check out the train transportation in Italy is to look at the Trenitalia website at www.trenitalia.it/en/index.html . It has an English site to help you out, but you can enter your origin, destination, and the hours you are looking to travel. At this point I am not sure if they will have the July schedule up yet, but you could look at an earlier date (same weekday) to get an idea of the schedule.
There are some trains that leave around that time of day (8-9AM) which will take you strait to Vernazza. For others, you will most likely have to change trains in La Spezia. But overall, it should take you about 1 hr. 45 min. or so to get there.
Have fun on your trip!