Long time smuggler here. Lots of good tips in the thread.
The biggest problem that makes scans happen is spending time within scan range of the patrol ships that orbit the station entry. That range is about 3 Km or so.
Once you are outside of that range, or inside the station, you're good.
If you are running cold, you can shrink that range to about 1.5 Km for small-medium ships. Maybe about 2 Km for a bigger vessel like a Python. But they can lock on still once you get close. Silent Running all the way to the slot is just overheating for nothing. You can shut it off at about 1.5Km away- they can see you anyhow. Since you become "visible" much closer in, giving less time for scanning is still useful.
So, when you drop out of Supercruise you will want to emerge well outside of the scan range. Hit the drop out as soon as you get the alert, because getting real close often plonks you straight into a 3 Km scan. I've seen the opposite advice: delay the drop in and get close because they have less time to see you. Don't be misled, close drops are a trap and that might be your issue right there.
If you are unlucky and there's a Police vessel outside the station that is suspicious, don't fly into the station. Turn round, boost away, and jump out into Supercruise for awhile. Pull up your Nav Panel, and lock onto any nearby system star. If he follows you out and starts to chatter about interdiction, just leave town and come back later.
If the approach is clear, this is my protocol: I have buttons bound to half speed, zero speed and max speed.
Set half speed.
Face Station, and roll to line up the facing plane.
Use vertical thrusters to square off the approach- you want to head in hot at a plumb 90 degrees to the facing plane.
Switch off thrusters before you visibly line up completely or you'll over correct even with FA on. Takes a little practise.
Cut your speed if you are straying too close - 4000 m distance is my limit.
Request docking preferably at max range ( 7500 - 7000 m), but do it once lined up and ready to run in.
Set pips to shields as you like. Weapons should have no pips.
I kill Flight Assist for more speed in. That's optional.
Set speed to max. Then, Boost in if ship is slow. Boosting in at low speed reduces your performance.
Hit Silent Running if paranoid, kill it at 1500 m out. No need for a Heat sink.
Cut speed and drop landing gear just before you enter the slot.
If you are too fast, and going to crash into the rear wall, flip over to face the exit and try to stop. That doesn't happen often, but if you just went back to a Cobra from a T7, well heh.
Not ALL the patrol ships can do scans. Some of them don't have scanners - if you get bored, loiter outside a station in a ship with no contraband, and target them. You can poke through their subsystems and see for yourself. That means there are gaps in the scan coverage, but we can't realistically make any use of this unless we scan them and figure out the holes in the patrol. That's feasible if you are pulling in stuff to a Black market system, and you know it well. Not feasible if you get a Shadow Delivery to somewhere new.
However, we can still leverage this a little: if you fly in just behind or aside a slower ship, there is a chance that the scanning patrollers might be scanning him instead. If there's space, you can slip past him on the wrong side as he's entering the slot.