Вот твоя книга. — Vot tvoya kniga. — Here is your book. (You are giving the book to its owner, so you use "vot", not "zdes'")
Смотри, вот дерево, о котором я тебе говорил. — Smotri, vot derevo, o kotorom ya tebe govoril — Look, here is the tree that I told you about. (Look! = you are pointing at the object, so "vot", not "zdes")
Здесь ступенька, не споткнись — Zdes' stupen'ka, ne spotknis' — Here is the sidestep, don't stumble. (The sidestep is always here, it doesn't move to other places. So this is the case when the position of the object is important, so we use "zdes'", not "vot".)
Thank you, it helped! But still I'm a little confused about the 2nd example of 'vot'. I mean, the tree is also constant in its position, isn't it?
I'm guessing that, for the tree the position is not being emphasized but the tree itself. This is the reason 'vot' is used. But for the sidestep, the position of it is important as you have mentioned. So, we use 'zdes'. Am I guessing right?
Вот is used as more of a demonstrative, like "Look at this" or "Here you go" without denoting that the apple is in any specific place, whereas the "here" you are using is used to reference a location, which you translate with здесь. If you know any French, it's the difference between "voici" and "ici".