The cable release you posted a picture of is the standard model that has worked wonderfully with thousands of cameras for many decades now. It's cheap and readily available, and does a great job.
Of course, in their wisdom many of the manufacturers of modern AF 35mm SLRs (maybe some DSLRs too?) have decided to leave a cable release socket off of their entry level cameras, or use a proprietary cable release socket that forces you to buy their expensive name brand cable release, which still does the same thing as the old school $10 cable release.
Since your manual says there is a cable release available at least you're not S.O.L. (as many entry level Nikon purchasers have discovered). Look on the other side of the lens than the side you have pictured. That's often where the proprietary cable release socket is; if it's not there check the manual. It's also possible that your camera uses a remote shutter release.
As mentioned above, you can get a device that straps around your camera with velcro, and adds a button with standard cable release threads that sits above your existing shutter release. These have always seemed sort of a pain in the butt to me, and the ones I've seen are a lot more expensive than a strap of velcro and a plastic button seems like it should cost.
Are you looking to do long exposures, or only trigger the exposure without touching your camera? If it's the latter you can use the self timer.