I think I need to write a long one here.. Skip what you know already.
First, anything starting with 'aap' (aap/aapka/aapki/aapke/aapse/aapko/aapne) shows respect(for elderly, by default) and is also formal while anything starting with 'tum' (tum/tumhara/tumhari/tumhare/tumse/tumko/tumhe/tumne) is casual(for same or less aged) and shows affection too.
There exists one very casual word 'tu' (tu/tera/teri/tere/tujhse/tujhko/tujhe/tune), which shows no respect at all and therefore used among close friends, with younger people or in anger(if). (But in few variations of Hindi (Haryanvi - for instance), people don't use 'tum' but 'tu' always and outsiders often get the wrong idea that they're being disrespectful which is not true)
Here tumhe and tujhe are additional words that are not very well formed and are same as aapko or tumko or tujhko in meaning but somehow used more often.
Now, let's see the usage with examples:
>> aap/tum/tu == you
"aap kaise hain?" or "tum kaise ho?" or "tu kaisa hai?" => "how are you?"
>> aapka/aapki/aapke/tumhara/tumhari/tumhare/tera/teri/tere == your
[these 'ka/ke/ki' are to show your relation to the object and are used according to the gender of object]
"aapka/tumhara/tera bhai" => "your brother"
"aapki/tumhari/teri maa" => "your mother"
aapke/tumhare/tere is a tricky one and used when there are multiple things related to you or something related to you is being used as an object in the sentence. (This is not always true and therefore it can be used to differentiate between a learner and an experienced Hindi speaker. I can explain but it's already too long.... anyways, see the examples to get an idea)
"aapke log" => "your people"
Not confused? Well. See this: "Main tumhare ghar jana chahta hun" => "I want to go to your house."
and this: "Main tumhara ghar dekhna chahta hun" => "I want to see your house."
Cont.. in comment..