I can give you two examples. Well more or less.
I was raised Catholic and they had prayers like the our father prayer, Hail Mary prayer, etc. They had different prayers for different saints and so on. Also they had the Rosary,etc.
Edit: Also Catholics have chants and also believe in saying the same prayer over and over again, one after the other.
I studied with Jehovahs Witnesses. They believe that the our father prayer was just an example, a template if you will, on how one should pray.
Edit: Jehovahs Witnesses believe that saying prayers like the Catholics do is not right. It has no meaning. When you pray it has to be personal and not repetitive.
Some believe you must be on your knees when you pray, other believe you can just pray anytime you want with out holding your hands together or getting on your knees, etc.
Edit: Some people feel you need to pray out loud, others feel you can just pray to yourself. Some hold their arms up, some close there eyes and so on. Some start rolling around on the floor while praying or worshipping.
These are only a couple of briefly summerized examples. I think this more or less sums it up.
In non Christian beliefs you sometimes have rituals and the like you need to do to (talk, pray, communicate,) with/to what ever god/godess/spirit/power you worship or believe in.
Edit: In Non Christian religions/spirituality, It depends on your beliefs and how you approach certain things. Of course then you have Magick and rituals that sometimes go along with that. There are to many variations to really get into and aren't relevant to Christian beliefs. So I wont go into that here.