Changing Domain Name

I have a wordpress installed to a domain (www.example1.org) but I have just purchased a new domain (www.example2.com) and want to change the domain settings for wordpress to my new URL. I have tried going through the wordpress helps but they don’t seem to be working. My new URL has no domain Hosting its just a purchased domain name. How do I completely replace my old URL, I don’t even want to use it anymore.

Thanks for your assistance anyone.