お + [verb ます-stem] + ください お + [noun] + ください ご + [noun] + ください
お~ください is a polite request, "please do ~". The verb goes in the ます-stem between お and ください – まつ待つ becomes おまち待ちください – and the form is honorific: it raises the person you are asking. You hear it from shop staff, in station announcements and on notices.
There is no て anywhere in it: ×お待ってください, ×お待ちてください.
A noun that names an action can go in the verb's place. Words read in on'yomi, such as れんらく連絡 and かくにん確認, take ご; native words take お. A few everyday on'yomi words take お all the same, でんわ電話 and へんじ返事 among them.
A verb that has a separate honorific verb builds the request from that one instead. みる見る is the one learners trip on, since its stem is a single syllable.