I've had to ask them to open the action when they tried to hand it to me. I will not accept a gun with a closed action.
I visually and, if possible, manually, check the chamber. I also make sure I can see daylight through the mag well.
These are almost absolute rules --the exceptions are that with some arms you can't lock back the slide or bolt (eg, old 10-22s) or stick your finger in the receiver to feel for a round (again, some .22s).
One thing I've noticed with the popularity of steel-cased ammo is that the laquered cases can be hard to see in dim lighting because of their dark color.
For one used to seeing nice, bright brass, the newer steel cases can easily fool me if my glasses are a little dirty or I'm particularly stupid that particular day.
Because of this, I've gotten really persnickety about looking in the chambers and groping in there with a pinky.
Bear in mind that simply cycling the action is no guarantee that there is no cartridge in the chamber! Extractors break, slip, extractor springs break or wear out, etc. etc.
Because of this fact, I had my first negligent discharge several decades ago with a 1911 whose extractor had broken. I cycled the action a couple of times, but a round was left in the chamber anyhow. I've mentioned this before, but I guess it's worth saying again, that the gun functioned normally since the residual gases blew out the empty cases and the ejector kicked them out just like normal. The negligent discharge was, however, in a safe direction.
I found the broken extractor hook on my workbench the next day, which is how I know the gun was functioning normally without an extractor hook.