Most of them work with the mouse already. In many aircraft you first have to set the turret/gun from the parked/cruise position to the firing position (i think the default command is ctrl+O), then you can move it.
In order to move the gun with the mouse, the clickable cockpit/mouse cursor needs to be disabled (default key to toggle the mouse cursor on/off is F10). Also, you can use the shift+F1 view on guns too now, making it easier to align the sights properly and aim.
That being said, there are some turrets that are behaving a bit weird. For example, the top turret on the Br.20 works with the mouse but the axis are reversed. I haven't tested the blehnheim's turret for a long time (first time i tried it i didn't know all this yet so i couldn't make it work), but i think i've heard of it having a similar bug or using different controls.
On the matter of different controls, there are turrets that make use of extra commands, for example the rear gun on the Stuka and the top gun on the He-111. In these gunner positions you don't just move the gun, you can also move or rotate the gun mount to change your arc of fire (i think the default keys for that are the arrow keys).
So, if you just jumped in a turret/gunner position that you're not familiar with, this is how you can work it out:
1) If it's enabled, disable the clickable pit/mouse cursor by pressing F10 and move the mouse. Does the gun move? If not, press ctrl+O.
2) Move the mouse again, does the gun/turret move? If yes, press the arrow keys to see if the mount is also movable.
3) If the gun/turret still refuses to move with the mouse, it might be that the controls are mis-matched, try using the arrow keys.
This is probably a case of how turrets are assigned in the game's engine. If a turret is assigned as a "gun position" it will default to mouse control, if it's assigned a "gun+mount position" status then it's mouse for the gun and arrow keys for the mount, but if it's only assigned as a "gun mount position" this could make it default to using the arrow keys. The problem with this is that while it's fine for altering firing arcs in a mouse-movable gun, it's not precise enough to actually aim the gun with if you are using powered turret.
This should probably help get you started and testing in-game, cheers
