I guess all learners of Georgian share this problem. The verbal system is extremely complicated so I doubt that any native Georgian speaker is able to give you a clear and comprehensive explanation. I didn't mean to put you off, it's a fascinating language. ქართული ენა ძალიან ლამაზია
My idea would be to learn a complete set of conjugation from some verbs. Not all the verbs use all the markers. It depends on what group they belong to and on the screeves (tenses).
Once you see the system after having learnt a few verbs you will be able to tell the patterns. At that point you will understand easier which marker means what.
for example the verb "to kiss someone" - კოცნა
მე ვკოცნი ... I am kissing ... (someone or something) ვ- means that I am the subject here.
Without any further context this sentence would need an object added, that's why I use the (...)
მე გკოცნი. I am kissing you. გ- means "you" as an object.
გ- is so to say stronger than ვ-. They both have the same asigned slot, but cannot be used both, so გ- takes ვ-s place.
ის გკოცნის. He is kissing you. გ- means "you" as an object
-ს means "he" is the subject. (It's almost like in English "he kisses")
In this case both markers use different slots. One is before the stem of the verb and the other is at the very end of the verb, so they don't conflict each other and are both kept.
This is just one example for one verb. Others work different. But I will make sense after some time, believe me
შენ მკოცნი. You are kissing me. მ- is the object marker for the first person singuar.
There is most of all times no subject marker for the second person singular
შენ ჰკოცნი / კოცნი. You are kissing him/her. ჰ- is one possible object marker for the third person singular. But it is rarely used nowadays, so in this example sentence you don't really have any markers at all. People would often just say კოცნი, without ჰ.
You can find a table on the markers on wikipedia. Look for the article on Georgian grammar and go to verb personality.
So if there are different possibilites for markers it depends on the verb which one is used or if there is any marker used at all. For example above we had ჰ- as a marker. Because the following letter is კ you have to use ჰ. It always depends on the following letter.
All of this is also explained in the article. If you want to read it and would like an example for something I can try to give you one.
Please keep in mind that this is only one example. Other verb groups work completely different.