I would suggest watching a few of the videos on YouTube concerning turning. In particular, Capn' Eddie Castelin's is very good. Some of his suggestions are great, i.e. letting the glue cure over night, others are OK, i.e. using a twist clamp as a pen vice. I know that a lot of people use them because they are cheap, but I can't imagine essentially ruining one just to use it as a pen vice. You can buy a great one for about 30$ from Woodcraft, and it is dead simple to use, plus it fits nicely on a drill press bench.
One other suggestion, pick a blank that is generally considered hard. Black Mesquite, Cocobolo, Lacewood, are good suggestions. I wouldn't try anything super hard like Ligum Vitae or Desert Ironwood unless you have carbide tools.
As others have said, sharp tools and light cuts are essential. One last thing, have fun!!
Here is the link to the video I mentioned above.
104 basic pen turning.mp4 - YouTube