I don't mean to discourage you but I would not "ask" for friendship. It sounds like too much pressure to put on someone (and kind of makes you sound desperate). I would immediately think that you have no friends at all and question that internally. I presume most people have made their friends already. If you are looking for a friend I would just be friendly and if you have things in common with someone a friendship will develop naturally. I don't think it is something that can be pushed. If a person backs away from your conversation then its best to let them go. There will be someone else someday that you will run into who will be drawn to you automatically. It just happens that way.