The first thing to do, is to go by http://secondlife.com/join and download a copy of the Second Life client. At the time of writing, Second Life works on a two-tier membership system. The basic tier is free for a permanent membership. This allows you to do pretty much anything in the game except own your own land and is more than adequate for just visiting the _blacklibrary. For information, the Premium tier that affords land ownership is $10 per month at the minimum level.
When you’ve installed the client, created an account and connected to the world you’ll have to endure a short tutorial. this involves making your way from one end of the starter-island to the other, picking up some basic skills along the way.
This is the Welcome Area, not a bad place to end up in. There is lots of free stuff available and player-mentors frequent the area if you need further explanation of anything.
When you’re through the orientation alt-tab back to this page and click this link:
…that should open your map screen in the Second life client and mark the position of the library. Click ‘Teleport’ on the map screen to be teleported directly to the front door.