Is it a simple transformer or is it a switching supply ?
It is a simple transformer. The label states that the output is 12V @ 300mA.
For all that, messing around with a 300mA supply is probably something you will regret. You will be better off getting a proper 9v 1000mA supply and using the 12v for something else.
Where do I get a "proper" 9V 1,000mA supply?
If, by your circuit error, the Arduino tries to consume over ~1A of current it will temporarily open its onboard fuse so you do have some level of protection there.
Is the fuse resettable?
Did you actually measure the output voltage ? Is it a simple transformer or is it a switching supply ? Is the output regulated to not exceed 12V ? Are you making any assumptions about actual output voltage based on the marketing of the product as a 12V supply? Have you confirmed that it is indeed 12V and not 14V ?
It's a wall wart. It came from a fluorescent tube emergency lantern. The lantern doesn't work. I haven't measured the output voltage. I guess that I should get a digital multimeter & measure the voltage of the wall wart, before I spend money on an Arduino, shouldn't I? In a DC plug, which is the positive & which is the negative? Is the outside of the plug negative or positive? I'd rather use a wall wart than a battery.
I just retired in February & I want to take up electronics as a hobby.