The aspect particle 过 (guo) is used to indicate that an action has been experienced in the past.
Subj. + Verb + 过 + Obj.
What this expresses is that the verb has been done at least once before, without specifying a particular time. 过 (guo) is used to talk about whether something has ever happened - whether it has been experienced.
In English, if you're asking a question and really trying to figure out if someone has ever done something before, we tend to use the words "ever" and "before." In Chinese, 过 (guo) alone expresses this, without the need for additional words.
Because 过 (guo) is used to talk about past actions, it should be negated with 没 (méi).
Subj. + 没 + Verb + 过 + Obj.
Note that when you translate these examples into English, "have never" [done something] is often more natural, indicating that someone lacks the experience of having done something, rather than just "have not" [done something].
To emphasize "never" even more, you can also use the word 从来 (cónglái).
You'll sometimes see 过 (guo) used together with 了 (le). This can be a little confusing, as it doesn't seem to be following the rules laid out above. For more on this special usage of 过 (guo), see the article on using 过 (guo) with 了 (le).