Although it can also work in the positive, 从来 (cónglái) is usually used when you want to express that you never do something (as a habit, or as a rule), or that you have never done something (it's not a part of your life experience). In either usage, 从来 (cónglái) may be shortened to just 从 (cóng) in casual speech.
When you follow 从来 (cónglái) with 不 (bù), you are expressing that you never do something (as a habit, or as a rule). It's often used as a way to refuse something, as in "I never drink."
The structure is:
Subj. + 从来 + 不 + [Verb Phrase]
Keep in mind that 从来 (cónglái) may be shortened to just 从 (cóng) in casual speech.
Use 从来 (cónglái) with 没 (méi) or 没有 (méiyǒu) (and 过 (guo) after the verb) to indicate that you have never done something (it's not a part of your life experience). You're talking about the past now, because you're talking about what you haven't done before, so 没有 (méiyǒu) is appropriate. 过 (guo) also makes sense, because you're making a statement about your life experience.
The structure is:
Subj. + 从来 + 没(有) + Verb + 过
Again, 从来 (cónglái) may be shortened to just 从 (cóng) in casual speech. Note that you can have an object or other information after the verb, but the 过 (guo) needs to come immediately after the verb.