As soon as Thunderbird starts up, you will see a few extra buttons on the bottom-left corner of Thunderbird - Calendar and Tasks. Clicking either button will take you to its respective view, Day or Week. Since the calendar is new, it'll be pretty empty. You can import a calendar if you've been maintaining one elsewhere.
Lightning supports importing of iCal-compatible .ics files, and comma-separated value files (.csv). Almost all web-based and standalone calendar applications should allow you to export your calendars to at least one of these formats. Just click on File > Import Calendar to import it. After it's done importing, you will be able to view your appointments and calendar entries using whatever view you prefer (Day/Week/Month).
Adding new entries is as easy as right-clicking on the appropriate date and selecting "New Event". It will open a small window where you will be able to specify how you want to store it. You can send invitations using the "Invite Attendees" button at the top. The description you type in will be sent as the message text to all recipients. You can also convert emails into calendar entries. If the email mentions a date, it will be taken as the meeting/appointment date. And you can also turn a calendar entry into an email. The integration with Thunderbird is very slick.
You can also publish this calendar online at compatible services like Google Calendar, 30 Boxes, etc. This will keep it synchronized between the two services, so you don't have to lug around your laptop everywhere. As long as you have Internet access, you can access your calendar online and make changes to it. All you have to do is right-click on the calendar and select "Reload Remote Calendars", which will synchronize your calendars between the two services.