The best way I've found to discover and use movable shapes is to derive them yourself from a handful of template shapes (specifically, the four main movable dominant 7th shapes). This is a system I worked out for myself from trying to make more manageable heads or tails out of a few diagrams (that lacked much explanation) in the book Ukulele Fretboard Roadmaps. Sadly, I haven't seen any other teachers focus on the 7th shapes rather than the triads—an artifact, I believe, of most teachers having come from the guitar world. But I know first-hand that, except in a relatively small handful of cases, starting with the 7ths is more consistent and simpler than starting with triad shapes. After all, the guitar chord naming system is really based around deviations from and extensions to the dominant 7th chord type.
If you want me to show you this shape derivation system, I'd be happy to videochat with you. If interested, start a private "conversation" with me and we can set up a session.
Oh, and please call them "movable chords" rather than "closed chords", which technically are chords with a narrow pitch span (relatively speaking), a different concept, and one used throughout the musical world. Similarly, what you may have been told are "open chords" are more properly termed "open position chords" (and here's the source of the confusion). Alternatively, I call them "fixed chords," which contrasts nicely with "movable", is snappier, and avoids conflict with "open" and "closed" in their more universal senses.