One leg of the antenna goes to the center conductor and the other leg of the antenna goes to the braided shield of the coaxial cable. The terminal block is just a way to make the connections, and it has two electrically separate positions. You can use any means of making the connection you have handy, as long as it is small compared to the wavelength.
(Vocabulary tip: the junction between the cable (feed line) and the antenna is called the feed point.)
However, it's worth noting that this is a poor design. Specifically, it has no balun — a device for converting between a balanced device (the antenna, which as you can see is symmetric) and an unbalanced one (the coaxial cable, which has an inside and outside conductor that are very different). This means that the shield of the coaxial cable will act as part of the antenna, and the performance will vary depending on how the cable is routed. It may pick up common-mode noise traveling from your receiving equipment along the cable, which can be a consideration when trying to receive weak signals from sources such as satellites.
You can read more about what a balun is and how it works in this application in the question Using a balun with a resonant dipole.