custom theme home page/blog separation

Hello guys i have build a custom theme and up until this point i have figured it out how to do it all on my own. The trouble im running into is that i want my home page of my site to look just like a home page no blogs or nothing. then i would like a link on my home page to take the user to my blog? how do i do that. I thought perhaps if i manipulated my home.php and index.php i can make my home.php my home page and my index.php my blog page but that does not seem to work?
I’m sure im not the first person with this idea. can anyone tell me how do i do this.
Thanks
Miguel