You'll want to give your calendar a name and description, both for you and for your customers. Follow the instructions on the page to edit your calendar.
One nice thing about Google Calendars is that you can authorize other people to edit events on the calendar or even give them administration rights. This means that you can create a calendar for your company and then give several people access to it to add and remove events.
If you want your calendar to be searchable in Google, you should make it public. If you're just going to make it visible on your website, you don't need to make it public.