HI Manuel,
In English, we have "in" and "into", and we're not always exact about the way we use these. Germans use *in* with the dative case to say "in" when they mean "inside a place" (or limited motion within an area). And, they use *in* with the accusative case to indicate motion
ins Kino gehen = in das Kino gehen = in + accusative case = going to the movies (going into the movie theater, there is movement, so the accusative case is used. The accusative form for Das Kino is the same as the Nominative form: *das*)
in dem Kino = in the movie theater (think of: sitting inside the movie theater. *Dem* = Neuter, singular, dative)
am = an dem. And *an* is just the preposition that is used to expressed "at", in certain situations - and in the case of days of the week, Germans use *an + day of week* to express "on + day of week* - ie, on Monday, On Tuesday, on the weekend, and even "at the end of the month". So, sometimes *an* is equivalent to english *on* and sometimes it means *at*.
1. Man kann in Detroit ins Kino gehen
- one can go (in)to a movie (theater) in Detroit (no article in front of Detroit, but if there were, it would be in the dative case)
2. Man kann in Detroit am Abend spazieren gehen
- One can go for a walk *in* the eveing in Detroit ( at the time of the evening, English= in the evening).
There aren't really any tricks that I've found to help with German prepositions. One needs to learn them with each expression.
But as for the difference between whether *in* or *am* and when each should be used - if you can answer why "in" or "at" is used in English, then you will have your answer. I'm a native English speaker, and I can't answer that question - at least not in a way that will help you in learning any language. It's just the way that languages develop. Most times, *at* = where one is located; and most of the time *in* = what surrounds an individual (He was in a bathroom at the office). Yes, he is *in* the office, technically, but that's simply not the way it is expressed in English (or in German).
You're an advanced English speaker according to your profile - do you understand the difference in English?