How to convert DV 720x578 (1:33:1) into 768x578 (1:42:1)?

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If you're using Avisynth you can see the difference between a 15:11 and 4:3 DAR using the CropResize script in my signature. It'll also display the corresponding input sample/pixel aspect ratios (obviously different for PAL and NTSC).

The script is being told to resize the width only (open the images in their own tabs for a full size version).
For a 4:3 DAR, the script can just resize to 4:3 dimensions (obviously).

CropResize(InDAR=4.0/3.0, ResizeWO=true, Info=true)


[Attachment 71755 - Click to enlarge]

For 15:11 the width ends up a little wider, although the script has also cropped a couple of pixels so as to resize to mod4 dimensions without aspect error (652x480). It calculates the resizing and cropping based on any input DAR you tell it to use though, so cropping and resizing without aspect error means "according to the specified input DAR".

CropResize(InDAR=15.0/11.0, ResizeWO=true, Info=true)


[Attachment 71756 - Click to enlarge]

In a perfect world there'd always be exactly 8 pixels of black each side, the input DAR would be 15:11, and after copping the 8 pixels each side, the remaining picture would be 4:3.

CropResize(0,0, 8,0,-8,0, InDAR=15.0/11.0, ResizeWO=true, Info=true)


[Attachment 71757 - Click to enlarge]

Whether there's 8 pixels of black each side or more or less, or even if there's no black at all, if in doubt I always assume the input DAR is 15:11 for a 4:3 video. Partly because I think it's usually correct, and partly because after cropping any black from the width and height, the remaining picture is be more likely to be at least 4:3.
The equivalent digital DAR for 16:9 is 20:11, but if in doubt I always assume the input DAR is really 16:9, as that tends to be the case.

As Sharc said, often the only way to be fairly certain is to take a screenshot of a frame containing a straight on shot of something round, or square, and draw a circle or square around it to see which DAR is closest to correct. Trying to do it by eye isn't reliable as the human brain is quite adaptive and if experience tells it a certain object is round it'll adapt quickly and make it round. Often there has to be quite a bit of distortion before it's obvious.

I did try to determine the pixel/sample aspect ratio used for a 16:9 bluray video once (720x480). The episodes were 1080p but the extras were 720x480. In order to match the aspect ratio of a picture from the extras with the same picture from the 1080p version, the input display aspect ratio turned out to be neither 20:11 or 16:9, but somewhere in between (20:11 should give you the correct pixel aspect ratio according to the bluray spec), so there's nothing to say either one is going to be exactly right anyway.