How you want to run things will be up to the GM as always. All the established lore in the universe isn't going to make a lick of good if the GM wants to go in a different direction.
My best word of advice is to look at real world examples and "in spess" them. This not only fills out logic solutions, but can also really add flavor and ideas you may not have thought about.
At he end of the day, smuggling falls into three rough categories: Stealth, Speed, and Subterfuge.
Stealth: The smuggler, through various means, attempts to avoid all detection. Real world you're looking at flying below radar, homemade submarines, heck there was even a former high school swim team that would just swim the product out to sea and back under the cover of darkness.
Speed: You get a fast aircraft or boat and blow past the customs people so fast they can't catch you. You see this one in the form of cigarette boats in things like Miami Vice. They meet a freighter out at sea, move product to the go-fast boats and they all blast in at top speed to different places. No way customs can stop them all, and if customs doesn't have go-fast boats of their own they may catch nothing.
Theres also an endurance version, where you don't go faster, just longer than customs can. You just keep flying till customs has to give up and go home to refuel.
Subterfuge: Probably the most common method. Here's where you hide the goods in secret compartments, Camouflage them to look like something else, or use bogus papers to looks like a legal transporter.
And there's mixing and matching. A crew got picked up last year using a vehicle they'd done up to look like a border patrol truck, running a stealth/Subterfuge hybrid.
So when you take those ideas and put them in space you can do some really fun stuff.