What is the correlation between wire guage and electromagnet strength

Whenever I have problems with the magnetic field strength of an electromagnet people tell to use a finer wire, I have some, its thickness is not more then the thickness of a hair, but whenever I use it, I have difficulty in connecting it with the battery because it's so thin it easily breaks off, and when I turn on the switch, it burns up instantly, maybe I am not using enough length of it.