The definition for 閉まる (which is actually found in many dictionaries) "be closed" is misleading. When I hear it, I automatically think passive tense, which it's not. It literally means "to close" but it's when something closes by itself.
ドアをしめる ([someone] closes the door)(transitive)
ドアがしまる (the door closes [by itself])(intransitive)
I did a quick J-google thinking I could find a better explanation. I found a
自動詞・他動詞 which did a good job of explaining it pretty well.
Transitive = has a direct object
Intransitive = has no direct object
If we look at the two example sentences I wrote above, or Mikecash's example, you can see that the transitive sentences have a direct object. The intransitive does not. What's far more important than being able to say "this is a transitive/intransitive verb" is having your brain know what works and doesn't work. In other words, know what's trans/intrans but not have to think about it. A lot of folks here are into learning the mechanics behind the language... something I ignored (and don't regret).
Just remember something like ドアをしまる is
incorrect. My suggestion is to start out making example sentences in flash cards (PM me if you want some help, I can write some out for you) and memorizing them. As Mike says, 'it's not hard once you get used to it'. It's like genders in other languages -- you eventually just 'know' what's right and wrong.