Well, since I talked about home yesterday, it seems only fitting to talk about leaving home today. Because what kind of story would it be if the protagonist never left on their adventure? Slice of life, I guess...
The most important part, I think, of that separation is contrast. The protagonist needs to immediately understand that they are someplace new, someplace different, and they can't get back without substantial effort. I think Dorothy summed it up best when she looked around said "Toto, I've a feeling we're not in Kansas."
It's a threshold, or at least according to the Hero's Journey it is. The protagonist needs to be someplace that, if not literally and physically different, is metaphorically different. Maybe culturally different. Just... something to take them out of their comfort zone.
But now what? You've stepped out on an adventure, so what's a protag to do? Well, that depends on what you want of your story. The story arc usually starts and ends with stasis. When your character leaves and enters the hectic, strange world, they need to be searching for a new stasis, a new normal. Maybe they just want to go home, maybe they want a new home. Maybe it's about saving someone, or perhaps it's just adventure for adventure sake. I think the point is, you need to know clearly and early what you character wants so you can focus on it.
So what makes that journey an adventure and not just a trip? Maybe I leave home and end up shopping in China town for groceries. That's strange and different for me, but is it really an adventure? I think the difference lies in a transformation for the person. Sure, I might have a good story about how had the opportunity to buy live eel for dinner, but I'm not that different afterward. After an adventure, though, I should be a different person. I need to grow or at the very least, change. My world view should be different, for better or worse.
Furthermore, there needs to be a significant obstacle. Sure, I might not speak Mandarin (yet) so I'll have a hard time grocery shopping, but at any given time I can just walk out and ask Siri where the nearest Wal-mart is. A real adventure needs to challenge your protagonist, grind them down and refine them, or, perhaps, break them.
Whether your character is out there to save the day, to seek their fortune, or just because they have no choice, a real adventure needs to reshape them and make them into someone that maybe even they wouldn't recognize.
Be Excellent To Each Other.
Keep your eyes open for my debut novel, The Paladin.