Is it possible to show the website for a given device?

You can also use the Device Simulator.

Switch to Preview mode, then from the View ribbon the Simulator button will be enabled and you can preview the page with a different device.

This is paricularly useful if you are using Responsive Web Designs. If you are using a custom device you may also have to switch the Device as suggested in the other answers.

You can switch the device manually using the built-in query-parameter sc_device in the url, followed by the name or ID of the device:

http://local.mysite.com?sc_device=tablet

http://local.mysite.com?sc_device={eb148a0f-220d-45dd-91fe-03b835e7e887}

You can use two things:

If its only about testing the device detection

• Change the device parameters in URL manually or use Sitecore ribbon menu with steps mentioned by @Dražen

If you want to test the device resolution and do click-thru testing

• Use Sitecore Device Simulator, you can use it to preview the website on some predefined devices resolutions. Here is the Sitecore documentation link

I have heard about Sitecore's AppCenter Page Preview Services and Device Detection Services but I don't have anything yet to share on that part.