You will be given the appropriate cable as part of the purchase and this should fit into you existing USB2 port, to allow full access to the drive from your laptop. However, you will only get USB2 speeds. To get the full benefit of a USB3 drive, you need a USB3 port. These can be added to most desktop PC's but, so far as I am aware, cannot be added to a laptop.
I have a very similar 2TB Seagate external drive. It may even be the same one because it ooks the same, but the product code is different. It is certainly faster than USB2, but the claims of UP TO 10 times faster you must take with a pinch of salt. It took about 8 minutes to transfer 80Gb of data. So long as you have a spare PCI slot, you can fit the USB3 expansion card. My Seagate drive had a USB3 cable included in the box. You will need one of those because existing USB2 cables will not fit the expansion card (although they do fit the actual hard drive).