First you go to the dashboard of tumblr, where you click on the title from your blog next to 'dashboard' at the top.
Once you're on your blog's dashboard you click on 'Customize appearance' at the top of the sidebar. It will bring you to the customize page for your tumblr blog. You can click this link as well and it will bring you to your main blog's customize page.
Once you're there, click on "edit html" and the code of your theme will slide open.
Here you see a bunch of crazy code what you need to delete, this is the code of you current theme. Select them all and delete it. You can select all text by holding CTRL+A for pc-users and for mac-users you hold CMD+A.
Must be as empty as this.
If you already have the code you can skip this step.
If you don't, you can find the theme code by clicking on 'download theme' at the themepage of the theme you would like. You can download the previewed themes as well.
Once the theme is downloaded you unzip and open it. If it's open you copy the whole code.
Paste the code in the emptry 'html' box where you deleted the last code. Don't forget to click on 'Preview' first. That way it updates the code.
After it's updated click on 'appearance' and the html box will slide back.
Click on save and reload your page. It's important that you reload the page, so please do that. Since tumblr build a new themepage you have to reload the webpage before you can see the full theme.
The theme is installed and you can now change the colors, add links and upload a background image. I mostly add a lot of options so check those so. Enjoy my theme!