The circuit is made up of three sections:
At the top of the diagram we have the CXA1645 IC - this takes a PAL RGB input, does all the matrix conversion on the signal and provides a composite output (we're not too interested in that), a luminosity output and a chroma output. S-Video consists of these separate luminosity (Y) and chroma (UV) signals.
R2, R3 and R4 let you tweak the red, green and blue levels separately. Even if you don't want to adjust the levels you will need a resistor between the input and ground there to let the capacitors discharge (otherwise the bright -> dark transitions won't be at all sharp).
Most devices that give you a SCART RGB output are lazy and don't provide you with a sync for that signal - you have to extract the sync from the composite input. The LM1881N takes the composite video from the SCART connector, extracts the sync and amplifies it a bit, giving you a composite sync output (i.e. the same as a composite video signal but without the actual video). This composite sync signal is then fed into the video encoder, which then adds it to the luminosity and composite outputs.
I found that the composite video input needed attenuating to get a good horizontal sync off it, so tweak R10 until the picture syncs properly. Of course if your video equipment gives you a proper sync anyway then you should be able to just feed that directly into the video encoder rather than needing the LM1881N.
Last but not least, we have the colour subcarrier generator. The 74HCT04 is a hex-inverter. We are only using 2 of the inverters on it - the first one is used with the parallel cut crystal across it to form a resonator. The second is used to drive the video encoder with that signal.
Remember to tie the unused inputs of the inverter to either the power rail or ground, otherwise they will float and the whole chip will probably start resonating, which will likely cause problems.
If the oscillator isn't working then you will still get video, just no colour.
I haven't tried running an NTSC signal through it, but in theory it should work. You will need to change R6 (pin 18 of the CXA1645) to a 20K 1% resistor, tie pin 7 of the CXA1645 to the power rail and change the crystal for a 3.579545MHz one.
It has been pointed out that the CXA1645 datasheet recommends placing a 2.2K resistor between the oscillator and the SCIN pin and a 47pF capacitor between SCIN and ground to remove high frequency components from the sync signal. This was omitted from my design by mistake and whilest it works ok for me without these components they should probably be included as they may improve the output quality and stability.