It sort of explains this in the tips & notes, but here's an example that might help.
Say you're going inside a restaurant. (Das Restaurant)
You are moving from outside the restaurant to inside the restaurant, so the case is not dative and instead accusative. "Ich gehe in das Restaurant" or "Ich gehe ins Restaurant."
Now say you are walking WITHIN the restaurant.
Your movement is all within the restaurant. Thus you are not moving from one place to another relative to the object we are talking about, so you use the dative case. "Ich laufe in dem Restaurant" or "Ich laufe im Restaurant."
Other things that involve staying inside the restaurant, such as sitting (like this example) will also take the dative case.
Therefore, the accusative case is used when there is motion relative to the object, and the dative case when there isn't motion relative to the object.
If your confusion stems from the earlier sentence "Ich bin in Amerika", I think it's still dative case, but because you wouldn't say "I'm in THE America" there is no article change as the article doesn't exist.
Somebody correct me if I'm wrong, and I hope this helps!