Well, if I remember well the way they taught me, changes happen between open syllables (ending in vocal) and closed ones (ending in consonant). Note the ending of kaupunki (city). In the nominative, the last syllable ends on a vocal (i), therefore he letter before is k. Then take the inessiivi (kaupungissa), the same syllable ends on a consonant (s - as you separate kau-pun-gis-sa, if I remember well, a syllable in Finnish can't start with more than one consonant), therefore the consonant 'k' becomes 'g'. In the meantime, it remains 'k' in th illative (kaupunkiin) because the syllable ends on a vocal. (kau-pun-ki-in)
Same, or partly, goes for most Finnish words that en in -i, where 'i' becomes 'e'. (e.g. saari [island] > saaren)
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