What sort of connection is used on this car remote antenna?
It looks like a very common 2.54mm (0.1") rectangular connector.

The most popular by market volume is Molex's C-Grid series.

You will need to buy (or already have) three things to make these connectors:

1. A housing

The housing is the connector's body. It is responsible for arranging the electrical contacts and protecting (or not) against inserting it upside-down (reversed insertion polarity). 

This is a Molex 0050579204. It will fit your application, but it is not keyed (mechanically protected against incorrect insertion polarity) like your current connector (couldn't find an exact match).



You can buy them here for about 1/2 USD each.

2. A pin-crimp insert

These are the electrical contacts that attach your wire to the device. They sit inside the housing.



You buy some here for a few cents each.

3. A pin-crimp tool

A crimp tool crushes the electrical spines of the pin-crimp insert into the wire (a process called "crimping"). Most home electrical sets have a crimp tool. The difference with the C-grid (and most smaller-diameter electrical crimp systems) is that more precision is required. Hence, better more expensive tooling.