Did you IVTC / deinterlace your DVD footage? If not, read this page
of the guide and the 'Analyzing the Footage' page it links to.
In short, you want your footage to be progressive before it hits your editing program, because doing it afterwards is very difficult. Fades and effects will mess up the field information, and because the clips are all chopped up the common three-frames-clear-two-frames-combed pattern is harder to find.
An AviSynth script is a series of commands that tells compatible programs what to do with a video source. You start out with a source filter and then apply transformation filters. A source filter is one that provides a video clip (or still image) for output. The common ones you'll be using are MPEG2Source, which is for loading the d2v file(s), and AVISource, which is for loading the Premiere export of the finished video. Transformation filters alter the video they're given, and they're what you'll be using for resizing, image cleanup, IVTC and deinterlace, and fixing any source-specific problems. A really basic script will go something like this:
#loads the d2v made from the vob
#restores progressive frames by matching fields
#removes duplicate frames from the now-progressive source
#a smoother. There are better ones out there, but this one is covered in the guide.
#sharpens and darkens lines, which is useful for anime. It's a one-size-fits-all filter that doesn't actually fit very many sources, and it's really slow as well.
#changes the framerate to 24fps. Premiere and other editors can have problems handling 23.976fps video. You can convert the audio too so that when you change the video back to 23.976 after editing it all matches up... but it doesn't matter if you forget because it doesn't make all that much difference.
I do not endorse the above script and use it only for demonstration purposes.
(I dunno, maybe that was a little too basic...)