I am wanting to add a 3D OBJ Model on a website, but I have absolutely no clue how to - google searches gives me options for in-browser games, but not this.
I basically just want a model that can be turned around with the mouse. Just like Microsoft's page for Surface. http://www.microsoftstore.com/store/mseea/da_DK/pdp/productID.300225600
You are looking for WebGL ... there is a lot of websites that offers to view 3D objects directly into browser, such as https://sketchfab.com/ or https://p3d.in/.
in Microsoft website they are using a image based plugin that simulate the product rotation, you have to take a 360 degree pictures and upload them into your hosting so that plugin work. I recommand to use a 3D model instead, in addition its supported on mobile
have a look at http://www.x3dom.org/, https://playcanvas.com/ (its not related but it'll do the job) hope this helps :)