Use it just like "it is not ... " or "that is not..." ie: "it ain't the right one " "it ain't right" (not fair, no justice or not proper, not correct) It's informal English, used everyday here. If you choose not to use it, recognize that the majority of American English speakers will.

The term "ain't" is informal slang and I suggest you avoid using it until you are very proficient in English and know the right situation to say it. In your phrase, "it ain't" what you mean to say is, "it isn't" or "it is not": It is not cold today. It isn't cold today.