CHANGE "/?cat=all" TO "/blog" PERMANENTLY

Hi, I have a general question about the URL.

Since I use a static site for a homepage and have a blog on the website done with wordpress as well, I wonder how I can create my blog, really also showing “/blog” in the URL permanently instead of the regular “/?cat=all”.

Does anyone know how and where I need to change code, in order to get this effect happen?

Looking forward to your answers,

Cheers, Arny