If you ever listen to Theresa May, the Home Secretary, when she occasionally pronounces on Scottish independence you'd be forgiven for thinking that the border was going to be turned into some ghastly concrete and barbed wire frontier post complete with machine gun nests and nasty border guards shouting for your 'papers!'. Or guys in black uniforms going through train carriages checking your passports. Scary stuff eh?
The reality of course is that you'll be able to cross the border exactly as you do at the moment. No border posts, not even a little hut with a brazier. Just the open road, as it is now. As an example, try crossing the border between Northern Ireland and the Republic (independent since 1921). It's just like crossing the border between Scotland and England. That's because we're all part of what's called the Common Travel Area, which states: "..passengers are not required to carry a passport or national identity document for immigration purposes".
Open borders are an integral part of the EU. Take a look below at the border between Belgium and the Netherlands. It runs through a cafe.