The GPS modules that you can buy for around $30, there are several different brands.
The antenna for these is a chunky square thing about 18 mm square and about 8 mm thick. They are usually a pink color for some reason that is unknown to me. For most GPS modules, the antenna is glued directly on top of the GPS microchip. Some of them have a cable connection so you can put the antenna somewhere else.
The GPS module connects to the Arduino by a serial connection, normally 4 wires, +5V, ground, RX and TX. Some of them have the Rx and Tx incorrectly labelled.
Using a USB to serial converter, you can connect the GPS module directly to your computer and use one of several free applications to interact with it.
The antenna itself is of no use to you. You cannot connect the antenna to an Arduino. The Arduino has no RF processing capability. The antenna is only useful when connected to a GPS module.