1. Domain and Web Hosting
Yes, you can get those @ GoDaddy.
2. Web Site Design
Yes, you can design your web site in Photoshop. It will be one giant graphic. You will have to either splice the images (the header, the footer, the background, the menu bar, the sidebar, etc) or save each one to its own file.
3. Web Site Development
This is where you take the graphics created in step 2 and embed them in the web site code. For this you will need another program. Notepad could do, but I recommend something like Notepad++ or Kompozer... or a combination of the two. If you don't know much about coding, look in to XHTML and CSS... and also check out w3c.org and w3schools.org - both very good web sites that should get you started on that part.
You can always come back for more help later.
Btw, once you did step 3, you can use an FTP client (like Filezilla) to upload your graphics and HTML pages to GoDaddy. Notepad++ and Kompozer also have a simple FTP client built in, so you could later on update your web pages with those programs.
I have just recently started looking into how to design a website. I'm basically clueless. I'm considering using GoDaddy for the hosting, but I'm trying to figure out the design part. I currently have Photoshop 7.0. Does anyone know if I can use this to completely design my website and then use GoDaddy to get it up and running? Will I need some other program to transfer stuff from Photoshop to GoDaddy?? Thanks for your help!!