How do I know which cases follow which prepositions of motion?

Unlike Latin, Classical Greek has more concrete rules on which cases govern which prepositions of motion. When dealing with motion towards (e.g. εἰς/προς - into/towards), the accusative case is used. Hence GCSE students may see a sentence such as βαδιζω προς την ἀγοραν - I walk towards the forum. Motion away from (e.g. ἐκ/ἀπο- out of/away from) is governed by the genitive case; τρεχω ἐκ της οἰκιας - I run out of the house. Stationary prepostions (e.g. ἐν/ὑπο - in/under) are governed by the dative; καθιζω ἐν τῳ ἀγρῳ - I sit in the field.