"Alguno" is an adjective, and so it must agree with the noun it modifies (therefore there's "alguno", "algunos", "alguna", "algunas"). "Algún" is its short form when it goes before a masculine noun.
It is used as "some" when it refers to someone or something as opposed to "none", to express a notion of "a little", when it talks about a way not specified...
·Aquí hay algunos alumnos que saben varios idiomas. -> Here there are some students who speak several languages.
·Vinieron algunas personas a la tienda, pero ninguna compró nada. -> Some people came to the store, but none bought anything.
·Algunos amigos nos ayudaron. -> Some friends helped us.
·Si tuviera algún conocimiento de matemáticas, podría ayudarte con tu tarea. -> If I had some knowledge of mathematics, I could help you with your homework.
·Yo no le dije nada, pero de alguna forma se enteró. -> I didn't tell him/her anything, but somehow he/she found out
It is used like "any" when it's like a "negative some" (sorry, can't think of a better way to explain)...
·¿Conoces alguna forma de aprender sin estudiar? -> Do you know any way to learn without studying?
·¿Tenemos algún libro? -> Do we have any books?
·¿No hay algún modo de resolver el problema? -> Isn't there any way to solve the problem?
I hope it's not too confusing.