You have this a little backwards. For kunyomi they are stand alone kanji or can have hiragana added. For example the verb Hanasimasu. 話= Hana. By itself this kanji can mean story, narrative, etc. if you want to make it a verb you write 話す。However, onyomi have to be used in combination with other kanji. They have no meaning by themselves. I'll give a good example after I get back home lol.

Onyomi is the Chinese reading of the kanji. And have no hiragana attacked and are usually in kanji compounds. For example 空港=Kuuko. See no hiragana is attached. However, you absolutely have to know the most common readings for kanji. Unfortunately, because there are no spaces in Japanese writing you will have to learn to differentiate particles and modifiers within sentences. For your example もう一度。It is pronounced mou-ichi-do. The do being represented by the kanji. So it's not onyomi. And yes mou is a modifier. If I say もう一度言ってください。This roughly means "can you repeat/say it again". Mou implies the again. I hope that makes sense. You have to read more Japanese to have a better understanding of when something is hiragana, kanji with hiragana, a particle, or modifier. Japanese does have punctuation so you can at least see when sentences begin and end. For example "今日は、本屋を行きます".