A Full Format will do a Quick Format, then go though every sector of the drive and test it, marking off any faulty ones (very rare) so they won't be used. A Quick Format will do the job in 5 to 15 minutes. When that is done, come back to this new Partition and RIGHT-click again and choose to Format it. When all the choices are made, go ahead with the Partition operation. You can create a second Partition or more in it if you want.) For this first Partition, make it the Primary or Active Partition, and NOT bootable because this drive is for data only - you already have a boot drive. If you do, when you are finished come back here and find the remainder shown as 'Unallocated Space'. You'll have a choice of how big it should be and most likely want to use all the drive in one volume.

RIGHT-click on it and, from the menu, choose to Partition the drive. Your new disk should be here with no letter name and no info. The lower one, which SCROLLS, also shows you other devices Windows does not yet understand. The upper one shows you only the devices Windows already knows how to use. I expect OP (damaster) and joses both have got this far. In the new Computer Management window expand 'Storage' if necessary and click on Disk Management. Click Start, RIGHT-click My Computer in the window, then click on Manage from the menu. 'The problem may be you're not looking in just the right spot.

Kingston disk manager