does he get a gun shaped lump of metal that does not work at all?
Generally, one gets a gun-shaped lump of metal which is actually made of ectoplasm and can be dispelled with a Counterspell. Maybe you can Construct a revolver that can "open" so you can pretend to load it with bullets). A wizard could even try to pretend to use a fake gun to hide the fact that he is using magic, but for that he could easily carry around an actual plastic gun and not worry about a thaumaturgic ritual.
Per YS 274, "Functioning objects of real technology are pretty much impossible (or more accurately, too much work to be worth it)." The best someone can get with Conjuring is 1-2 moving parts, or maybe something which animates as if alive. We're talking scissors, pliers, a cigarette case, a box, maybe a simple folding knife with no blade lock. A moving creature sidesteps the "moving parts" limit, but still costs extra shifts.
So in the absolute fullness of the rules, a modern gun (which can have around 34 moving parts) could theoretically be made, but it would have an insanely high Complexity and require a lot of knowledge about how the tech works, and to make up that Lore Declaration, your Wizard is assumed to be doing magical shopping or engaging in any other number of skill checks which themslves could have resulted in a real working gun and bullets. Much easier to do any other number of things to get a gun when you need it. See Kommisar's response above. Also, see "Can I Conjure a Sword" on YS 275.
Now, what some folks have been monkeying with is trying to Summon an actual real item to their location using magic. But then you get into Teleportation rules, and it gets crazy.
But ultimately, what Wizards are conjuring are Things that need to take up space, be physical, and look real. Like a bridge over a chasm (but running water would be tricky). A barricade. A wall where there wasn't a wall before. A fake house. A fake dragon. A field full of frogs. An Ectoplasmic Shell for a Spirit. Fake money (although the time:investment ratio is skewed seriously the wrong way, so it's probably best to simulate a particular, important coin, like a Denarius, rather than Loads of Money. Anytime something needs to be there but couldn't otherwise be there because it would be Impossible.
A lot of these things could also be done with Illusions, but would have no substance. Conjuring is for substance.