They try to sell you a boatride to Comino and the Blue Lagoon from most of the harbours around and in Sliema, but it is very expensive and you will not have much time left for Comino after a long boatride. Take a Bus to north of Malta, the harbour with the Gozo Ferry line, and on the right side you will find a small company that drives between Malta and Comino for a few Maltese Lira, you pay only 50 cent for the busticket. I think that they wanted something like 12 Lira for the boattrip from Sliema
When you go to Comino don;t roam about alone, always go with another person. The place is very safe and there are no dangerous animals however the place is very barron. In Summer it gets very hot and wandering alone on the island is not safe because it will be hard for people to notice you. The ground there can be very rocky and spikey and the island has loads of small caves and inlets. There are no hospitals or people who can help you, besides it will take ages until someone comes by helicopter or by boat from the closest hospital which is in Gozo and not always very efficient so be careful!