Hi Sue

I wasn?t sure what you meant by register so I?ll cover what I know :)
I looked it up on Register.com and it looks like artforyourlifestyle.com is taken but it?s set to expire on June 15 2007 so you might have a chance to grab it up. I did see that the others are available (.biz, .net, etc.) so you still might be able to get something good.
As far as registering it with you state it depends on what state. Here it only cost $10.00 and I printed out the form online and mailed it in and got a certificate in a couple of weeks. A google search for ?How to register a business name in {your state}? pulled up the information for me. The site also had a search so I could see right away if it was taken or not.
For patent or trademark, if you want to take it that far, you can search here http://www.uspto.gov to see if it?s taken and if not you can register it yourself.
Hope some of that info help and good luck!