Knowing when to use certain prepositions
I am confused about when to use certain prepositions.

I keep reading and hearing "Don't just learn the prepositions, because they don't line up with English; just know which to use with each verb", but there are in fact times where there is no verb! Like times where you don't have a sentence. For example, on electronic interfaces. Even here on italki! I don't understand how to use them and I am always so confused. Like what is the difference between an and auf, and what about an and bei, and bei and mit, I wish I had someone tell me. For example: What's the difference between "beim Eiscafé" and "im Eiscafé"? Does someone have at least a tip for knowing them? Because I actually learned what they mean and still can't distinguish between most of them.

I'm not only asking about those I mentioned, I am asking about all of them!

Question

Knowing when to use certain prepositions
I am confused about when to use certain prepositions.

I keep reading and hearing "Don't just learn the prepositions, because they don't line up with English; just know which to use with each verb", but there are in fact times where there is no verb!  Like times where you don't have a sentence.  For example, on electronic interfaces.  Even here on italki!  I don't understand how to use them and I am always so confused.  Like what is the difference between an and auf, and what about an and bei, and bei and mit, I wish I had someone tell me.  For example:  What's the difference between "beim Eiscafé" and "im Eiscafé"?  Does someone have at least a tip for knowing them?  Because I actually learned what they mean and still can't distinguish between most of them.

I'm not only asking about those I mentioned, I am asking about all of them!

Answer

You are right: Prepositions don't always come along with verbs, but also occur in expressions without verbs. 
The problem is: There is no comprehensive explanation on which preposition can be used in which situation. You can ask why a certain preposition is used in a specific situation, but then there are cases which look similar but require a different preposition. (It's the same problem for Germans who learn English BTW). The only way to master these is: First: relax, and don't try to understand it all at once. Then read and listen a lot, and over a certain time, you get a "gut feeling" that will tell you which preposition is appropriate in which situation. It simply takes time.