When I practice the MILD technique I do it the usual way, by repeating an intention to myself over and over until I fall asleep.
What I’m wondering though, is - how are you supposed to repeat it?
Is it effective to actually speak out your intention, or should you only repeat it in your head?
In your head. You could do it out loud a few times, but the point is to get an intention set for when you fall asleep. I don’t know many people that can fall asleep while talking 
Indeed, the reason I was wondering was because I kind of felt like repeating it verbally would have a greater effect since you also heard yourself saying it, and that you would eventually become so tired that you fell asleep while still repeating it out loud;
think of it like reading a school book or something out loud compared to reading it in your head - reading things out loud tends to makes things easier to memorize. 
But of course, it’s probably much easier to fall asleep properly if it’s quiet.
One thing to consider is that you don’t have to do this just before you fall asleep. You could repeat your mantra to yourself several times throughout the day. That way, it’s a consistent theme and not just one you have right before falling asleep.
I’ve just started using an autosuggestion mantra right after I RC (and I’m RCing quite frequently). We’ll see how this combination technique goes in a few days hopefully. 