You're right, a lot of English nouns can be turned into "slang" verbs. Friendzone is a noun. It doesn't just mean to be friends with someone. There is more context to it. It means one person wants more than a friendship, they want a romantic relationship, but the other person only wants to be friends. So there can be a negative feel to it. It is more common among high school and maybe college aged kids, but you really don't hear adults use that noun. The verb form would be something like "to be friendzoned". This means "to be put into the friendzone". For example, say you went out on a date with somebody and at the end of the date, they said "let's just be friends". You have been friendzoned.

It's a slang word that means someone of the opposite sex preemptively tells you that you will not be a sexual partner. For example, say John is totally attracted to Susan. John drops all sorts of hints, makes sexual jokes, stalks her on Facebook and follows her everywhere. Then Susan tells him that she thinks he is a total sweetheart but they should just be friends. John could then say to his pal, "dude, I totally got friendzoned"... Unless you plan to preemptively reject someone as a future sexual partner, I think it is safer not to use this word.

That is very good advice, Mike.

Brian and Mojave both give good answer. A simpler -- and better -- answer is this: Don't. Please. In fact, don't use it at all.