SATA HDD's can be used without issue in a desktop, you may need to purchase a 2.5" to 3.5" drive bay converter, if desktop doesn't have mounting points for 2.5" HDD's
Yeah there's two ways you can do this - either purchase a external USB drive enclosure (like this: http://www.newegg.com/Product/Product.aspx?Item=N82E16817366014 ) and install your HD into that, or you take your laptop's HD and buy a 2.5" to 3.5" mounting bracket (like this: http://www.newegg.com/Product/Product.aspx?Item=N82E16817994141}. With the USB enclosure it works just like a regular USB HD. With the mounting bracket you will need to go into Windows and use the Disk Manager to find the drive and assign a drive letter before use.
If you're using it as your primary HD you will need to remove all existing Windows files and install the OS fresh. Be sure to back up your data.