This would actually be a pretty easy modification, if all we had to do was tap the audio and video signals going into the RF modulator (that big rectangular metal canister at the upper edge of the CPU board)...  Unfortunately, it isn't quite that simple; your TV set's A/V inputs don't have the same impedance as the RF modulator does, and just tapping the video signal may load down the Intellivision's video circuitry too much to get a stable picture.  Fortunately, a relatively simple single-transistor amplifier circuit is all that's needed to take care of this problem:

PARTS LIST:
C1, C2, C4, C5	100uF, 25V aluminum electrolytic
C3	10uF, 25V aluminum electrolytic
C6	0.015uF 25V ceramic (optional)
Q1	2N3904 small-signal transistor
R1	1.6K 1/4W 5% resistor
R2	2K 1/4W 5% resistor
R3	10 ohm 1/4W 5% resistor
R4	75 ohm 1/4W 5% resistor
You will also need: a piece of perfboard about 1.5" square; some shielded coax cable (about 24-30") and some regular hookup wire; a pair of panel-mountable RCA jacks (such as Radio Shack #274-346)

For those of you not familiar with electronics, this is what's called a common-collector amplifier, also known as an emitter-follower since the output at the emitter will always be one diode-drop (approx. 0.6V) less than the input.  This circuit is a staple in electronics designs, as it's a cheap and simple way to do signal-buffering and impedance matching.  Layout and construction isn't critical; you can build it on a bit of perfboard with point-to-point wiring.  All of these parts are common enough that even Radio Shack should have them – if not, you can get everything from All Electronics.  Total cost should be less than $10.

Once you're finished building it, you should have something that looks more or less like this.

You may be wondering why C6 is described as "optional".  This was one of the contradictory / inconsistent bits I mentioned earlier; some of those who had tried similar circuits said that the colors seemed too strong and "harsh" without this capacitor, while others said it wasn't needed.  It didn't seem to make much difference either way on my TV, so may depend on your particular TV set and personal tastes, so all I can suggest is try it and see what happens.  If you don't like the way the colors look, try adding this capacitor to mute their intensity a bit – you might have to experiment a bit to find the right value for your particular TV, but 0.015uF is as good a value as any to start with.  If the colors are too strong, increase the capacitance; if they're too weak (or the picture goes to black-and-white), reduce the capacitance.