Remove the driver's-side under-dash flat plastic panel with a Torx screwdriver (20-bit head - you only need to remove the three screws at the front edge).

You should see several relays plugged into the circuit board. Relay 8 is in the second position (from left to right) of the second row. (You may not have a relay in position one of this row.) Locate the relay and simply unplug it by gently pulling it out.
On my '98 Beetle, it looks like this (the quarter is for perspective): it has the large, white number "173" on it.

There is one unintended consequence to this procedure -- when Relay 8 is removed, your "Parking Brake On" warning light in the speedometer is disabled.
VW has linked the DRLs to the Parking Brake switch and warning light. (When your NB is running and your Parking Brake is "on"-- your DRLs are "off". Releasing the Parking Brake turns the DRLs "on.") So, when you pull Relay 8, the Parking Brake warning light no longer works...not a big deal, but I just wanted you to know. (There is a quick fix which I'll explain below.)

The whole procedure should take you about 10 minutes. And should you ever wish to re-activate your DRLs, simply reverse the steps outlined above and plug Relay 8 back in.

Take the top off the relay by gently prying the cover from the base - it's attached at the base on two sides. A small-bladed screw driver should help you work it off.

With the cover removed you'll see two circuit "switches" (one is open, one is closed). Take a look at your Parking Brake. Was it UP or DOWN when you pulled out Relay 8? If your PBrake is ON, you want to insulate the circuit that is "open" - in other words, the two contacts NOT touching. If your PBrake is OFF, insulate the circuit that is "closed" - the two contacts ARE touching.

(The two circuit switches control the DRLs and the Parking Brake Light. Depending on where your Parking Brake was when you removed the Relay either the DRL switch or the Parking Brake Warning Light switch will be closed [activated].)

Take a small piece of electrical tape and insert it between the two contacts to isolate them. Tape it in place so that it won't fall out.

Put the cover back on the relay and gently plug the relay back into the circuit board behind the headlight switch. You're done. That's it!

What you've accomplished is the defeat of the actual "switch" that turns on the DRLs. Since those contacts have been prevented from touching, your DRLs cannot come on. But, everything else works, including the Parking Brake Warning Light, which is controlled by the circuit you did not modify inside the relay.

Naturally, if you later decide to reactivate your DRLs, reverse your steps and remove the electrical tape from inside Relay 8, then plug the relay back into the car.