This is assuming you are using the composite video to play on your PS2. I'm also assuming that there aren't any other differences in equipment in different parts of the world (me being in the US and you apparently in Australia). Also note that I myself don't own a PS2 nor have I ever really used it much, but it should be the same for any console really. I'll also assume you don't have not-so-old equipment. So everything I mention here I'll assume your equipment has as these are fairly standard nowadays.
You'll need 2 things first, a "male-to-male" RCA-cable and a video recording device. Here, I'll use a VCR as an example.
To be able to play your PS2 on your TV, you will probably have one of many different setups for it to work. A common one is to just connect your PS2 directly to your TV using RCA video cables (the yellow/white/red set of cables).
The cables will usually go to (one of) the "video in" connections in the back of the TV to your PS2 in the appropriate connector. It will probably look like this (other unrelated details left out):
And this is how you can play your games. The signal comes out of your PS2 and goes into your TV. You can see the results on your TV.
Now to the recording. Your TV will probably have a "video out" connection too. This would allow the signals your TV receives to send it out to another device. We want these signals to go out into our recording device so it can record it. We could use a VCR to do this. Record it on tape and you're good to go. To connect it, connect the RCA cable from the TV's "video out" to your VCR's "video in" (it might be called "line in" instead). So it should look like this in the end:
Once you have this all set, all you have to do is start playing, load a blank tape into the VCR and start recording. Then you can share the tape with your friend. Simple right?