How do you master adpositions, besides memorisation?

Question

Summary of Question: Many popular books only suggest memorisation (useless for many) and do not explain adpositions and their uses. Beyond memorisation, how else can a language learner master the acquisition of adpositions? Though adpositions are Functional Morphemes, the failure of memorisation forces me to pursue more effective methods, such as Googling 'semantics of [insert language here] prepositions' and trying to understand the resulting linguistics papers.

Optional Supplement: The omittable following is published in 2 sources identically:
_{p 2, Applying Cognitive Linguistics to Learning the Semantics of English to, for and at: An Experimental Investigation, also by Prof Andrea Tyler, C Mueller, V Ho.
pp 130-131, Cognitive Linguistics and Second Language Learning: Theoretical Basics and Experimental Evidence.}

Language teachers and researchers have long recognized that the acquisition
of prepositions poses major challenges for second language learners (e.g., Celce-Murcia and Larsen-Freeman, 1999).
One reason for this is that the semantics of prepositions are notoriously difficult to characterize. [...] Additionally, prepositions tend to develop a complex set of extended meanings, for instance, over has developed at least 16 meanings, many of which do not appear to be systematically related. Although linguists have long been aware that prepositions develop complex polysemy networks, the meaning networks surrounding spatial markers (and the systematic processes of meaning extension from which they result) have only become the foci of linguistic inquiry
in the last 20 years. Even the best descriptive grammars and dictionaries present
the multiple meanings of spatial language as largely arbitrary. Traditional accounts have represented the semantics of English prepositions as arbitrary (Bloomfield, 1933; Frank, 1972; Chomsky, 1995). Consequently, pedagogical treatments have often suggested memorization as the best strategy. Studies show that accurate use of spatial language is one of the last elements learned and many highly proficient L2 speakers never attain native speaker-like use (e.g., Lam, 2009). Indeed, Lam found that L2 Spanish learners made virtually no gains in their mastery of the prepositions por and para over the course of four years of college Spanish.

Answer 1

You don't need to actively memorize rules to learn how to use adpositions (prepositions / postpositions); but a lot of time is needed to acquire the patterns. I think a combination of passive and active methods is most useful:

1. Input

Get lots of input, by reading a lot and listening a lot. If you're trying to learn the rules of which adposition to use through a grammar or exercise book, you're understanding of the rules will not be deep - it will be technical, and you'll have difficulty seeing the subtleties that exist (grammar books often paint the differences between forms in black and white, when they are often quite gray). When you get lots of input, you'll see adpositions used properly, and you'll learn a lot of the patterns subconsciously.

2. Notice patterns actively

If you're getting lots of input, try to notice the patterns you see regarding the adpositions. The patterns you notice yourself are often better learned than the patterns / rules explained in grammar books. When you do this, remmeber that the patterns are not strict rules, and that there are often very subtle differences.

3. Get Feedback

Try to get feedback regarding your usage of various adpositions. Input is great, but some of the subtle differences can be very difficult to pick up on with input alone. If you don't get any feedback, your mistakes will fossilize if you don't realize that you're making a mistake. So you can try writing example sentences using various prepositions. Try to use them in borderline cases where you're not exactly sure which one to use. Ask a native speaker to give you feedback: which are definitely wrong, which sound unnatural or perhaps imply the wrong meaning, and which are correct. If possible, ask a native speaker who is "linguistically literate" - someone who can explain why your mistakes are wrong.