How can I wire a RFID antenna to a Raspberry Pi?
You can't connect the antenna to you Raspberry Pi.  It is an antenna, not an RFID transmit and receive module.
Look at the other picture that shows a complete module.  It has a chip that handles all the RF stuff, and communicates with the Pi over the SPI bus.
Your antenna has none of that.
Your antenna is just the part of the module with the big wire loops.

It is probably possible (with some really clever software, a few transistors, and some other bits and pieces) to make your Pi do what is necessary to drive the antenna and receive the RFID data.
It wouldn't be easy, and I know I couldn't do it.  Asked the way you have asked it, your question says you aren't up to it either.
Get an RFID module and move on.