ご + [noun] (Sino-Japanese) お + [noun] (native Japanese) お + [i-adj] お/ご + [na-adj]
御 goes on the front of a noun or an adjective that belongs to the person you are talking to or about, and shows them respect: your name, your family, your being busy. Before a Sino-Japanese word (a kanji compound read the on'yomi way) it is ご; before a native Japanese word it is お. Both are normally written in hiragana.
The prefix shows respect to the owner, so your own name, family or order go without it. The waiter says ごちゅうもんご注文; the customer says ちゅうもん注文.
Your own action does take it when it is done for the other person: ごれんらくご連絡します, "I'll get in touch with you".
ご goes with Sino-Japanese words: ごかぞく家族, ごじゅうしょ住所, ごいけん意見, ごけっこん結婚. お goes with native words: おなまえお名前, おかねお金, おてがみ手紙, おみずお水.
A good number of everyday Sino-Japanese words take お anyway: おちゃお茶, おでんわお電話, おしょくじ食事, おりょうり料理, おべんきょう勉強, おげんき元気, おたくお宅. A few native words take ご: ごゆっくり, ごもっとも. These have to be learned word by word.
These go beyond showing respect to the listener.
Some words carry お whoever owns them, because the plain word sounds blunt: おちゃお茶, おかねお金, おみずお水, おべんとうお弁当. In a few the prefix has fused with the word and cannot come off: ごはんご飯, おにぎり, おなか.
Family words take お when they refer to someone else's family or when you address your own elders: おとうさんお父さん, おかあさんお母さん, おにいさんお兄さん, おねえさんお姉さん. Younger siblings never do: おとうとさん弟さん, いもうとさん妹さん.
An adjective that describes the other person takes the prefix: おいそがしい忙しい, おわかい若い, おげんき元気, ごしんせつ親切, おじょうずお上手. A な-adjective with the prefix pairs with the honorific copula でいらっしゃる.
Words that already start with an お sound (おいしい, おおきい大きい), long words (じゃがいも) and most loanwords (えれべえたあエレベーター, こうひいコーヒー) go without. Shop staff do put お on a few loanwords – おといれトイレ, おびいるビール – but that is service speech, not something to copy.
お + ます-stem builds the honorific おまちになるお待ちになる and the humble おまちするお待ちする; ご + a する-noun builds ごりよう利用になる and ごれんらくご連絡する. Each is its own grammar point.
In a handful of set words 御 is read differently: おん in ごしゃ御社 ("your company") and おんちゅう御中 on an envelope; み in religious and imperial words such as おこころ御心. The meaning is the same: respect for the owner.