[verb ます-stem] + たい [verb ます-stem] + たくない [verb ます-stem] + たかった [verb ます-stem] + たくなかった
~たい means "want to": it states your own wish to do something. Take ます off the verb and put たい on, then です to keep it polite.
With たい on the end, the word changes the way an い-adjective such as たかい高い does.
×食べたいません and ×食べたいではありません are wrong. The ます has gone, so there is nothing for ません to attach to, and ではありません is for nouns.
A statement with ~たい is about the speaker. With か on the end, it asks the listener what they want.
A plain statement with ~たい does not say what someone else wants. ×母は日本に行きたいです is wrong: you cannot speak for your mother's feelings as if they were your own. Report what she said instead.
Or use ~たがっています, which describes someone who is visibly keen to do something.
English invites with "do you want to…?". いっしょに一緒にえいが映画をみたいです見たいですか is not an invitation in Japanese; invite with ~ませんか.
Asking a teacher, a customer or anyone above you what they want with ~たいですか is too direct. Offer the thing itself.
These go beyond saying what you want to do.
The thing you want to eat, drink or see can keep を or take が. Both are correct and mean the same; が puts a little more weight on the thing.
Only を can change. に, と and で stay as they are, and ×日本が行きたいです is wrong.
~たい goes on verbs only. To want a thing rather than an action, the word is ほしい, and the thing takes が.
Between friends, です is dropped.