[Reycer]

Well honestly it doesn't get much more clearer than what is in the manual. If you want to download the style you made just go to admincp--->Styles and Templates--->Style Manager--->and click on Download next to the style you want to Download.

Style: Layout (as in your case)
Product: Vbulletin
Title: Whatever you want it named, in this case prolly "Layout"
File Name: (I would just leave it alone)
Get customizations made only in this style (Should be ticked)

Click on Download.

Now make sure that you download the images folder off of your server for the style that you made, you will need this.

Install:
Upload the images to your new forum folder on the new server.
admincp--->Styles and Templates--->Download/Upload Styles

Now in the Import Style XML File box, click on browse and find the XML that you downloaded from your test forum. If both boards are running the same version of Vbulletin, then Click on Import. Otherwise, click on Ignore Style Version and set it to YES. Click on Import. If you've uploaded the images folder to the correct location on your server your new style is ready to go.