Here's how it works in your examples:
* Disappoint: "Appoint" means to assign or designate. "Disappoint" means to *not* fulfill an expectation, or to fail to meet a desired outcome. So, "dis-" adds the sense of "not" or "lack of."
* Disappear: "Appear" means to come into view. "Disappear" means to go out of view, or to cease to exist. Here, "dis-" indicates the opposite of "appear."
In many cases, "dis-" can be used to create a negative or opposite meaning for a word.