I mostly understand the glottal stop (ʻ), but I am not sure how to pronounce a word, like ʻŌlelo, when it begins with a glottal stop. Do I begin to pronounce the Ō, and then briefly stop before continuing on (ʻŌ - pause - Ōlelo)? Or do I pronounce it in an entirely different way?
In English we actually close the glottis before saying a word that starts with a vowel. That is all that's required when saying a word that begins with an ‘okina. So basically, no special effort is required. Saying a word that starts with a vowel and not an ‘okina is the thing that takes more effort and attention.
When it's at the beginning of the word, basically "ignore it," as the glottal stop kind of natural when beginning a word or sentence with a vowel. If you were to have a word before 'ōlelo, though, you have to make the stop, otherwise you're changing the word and it can be confused for something else. If you were to say "E ola ka 'Olelo Hawai'i," for example, you need to separate the O sound from Ka in order for it to be understood as language. If you didn't, you'd say "Ka ōlelo," where it sounds like "kao" instead of "kah-o." Does that make sense? If you were to move the ' and say it after the O, you'd be saying o'olelo, which... Well, wouldn't do you much good. Haha! So, yeah... Just "ignore it" when you're starting a word with it, but remember it when you have words before it.
For everyone having trouble getting the kahakō over the "o" on mobile (I know Samsung does not have it on the standard keyboard, not sure about Apple), download GBoard and enable the Hawaiian keyboard. This makes the kahakō available over all letters, as well as the ʻokina. Hope this helps!