The most basic method is to "bob" deinterlace, which is more of a form of "interlace simulation" - you take the original fields, place each one in the appropriate image lines of a separate frame of video, then perform some type of interpolation of each frame for the in-between lines. More advanced algorithms exist like yadif, that do some amount of motion detection to determine which parts of the image require deinterlacing, and which parts can be essentially done with a "weave", which is just taking part of the image data from a combined 30fps frame containing two fields.

The effective rate for 50i or 60i video, in terms of motion fluidity, is 50 or 60fps. Just because it's half the resolution per field doesn't mean that it's not a "frame" of video in abstract terms, just that it's not a "frame" in the jargon (because fields by definition are half a frame).

It is impossible to decimate a video from 50/60i to 25/30p without losing half of the motion fluidity, even if the properly interlaced source video is technically 25/30fps.