I really don't know which one to use in which situation. Is it about the situation? The type of object?
Same problem with the ones for "to open": 開ける、開く
Also, am I missing one of the verbs for "to open"? Because I've only learned two for that one, and three for "to close"
Thanks!

For 開ける and 開く, it's a matter of what is doing the opening. 開く is something that a noun does on its own, i.e. "the door opens"; 開ける is something that is done to a noun, i.e. "I open the door".

For the verbs translated as 'close', two of them are the same scenario (閉まる and 閉める), but I don't really know how to explain the difference of 閉じる well, so I'll let someone else do it.

I suggest reading up on transitive and intransitive verbs in Japanese, as well as passive vs active voice. It should help clear things up

EDIT: after a quick Google search
http://forum.koohii.com/showthread.php?tid=4485
(As a useful tip for using this site, if you're looking for something on this site in Japanese, use Google's site search feature; the forum's search function only supports ASCII)

EDIT2:
From the thread above:

Ryuujin27 Wrote:【１】「閉める」は、上下、左右、前後など直線的な動きによって開いていた空間をおおう意だが、「閉じる」は、直線的な動きばかりでなく、ちょうつがいのような円弧状の動きによって空間をおおう意でも使われる。また、「会を閉じる」「店を閉じる」などは、行っていた集会、営業など機能をやめる意もある。別に、「幕が閉じる」「水門が閉じる」などしまる、ふさぐ意の自動詞もある。

Basically, 閉じる suggests a closure resembling an arc (books, eyelids, etc) and has an additional meaning of closing a meeting or business.

But you can say "本を開く" right? And the book doesn't seem to be doing that on its own.

I think your missing one for 'to open' is ひらく, that is if when you wrote 開く you meant あく.
Or あく if you meant ひらく when you wrote 開く

Like sholum said the difference between あく and あける is a transitive vs intransitive problem.
ひらく vs あける however is a matter of using the correct one for the correct type of action.

You can find lots of varying and conflicting explanations on Google with a quick 'あける　ひらく　違い' search, but I like this one the best http://homepage3.nifty.com/recipe_okiba/nifongo/074.htm

And again, しめる vs しまる is a transitive vs intransitive problem.

But しめる vs とじる has the same problem as あける vs ひらく in which you just kind of need to get used to which verb goes with which kind of actions.

After a quick search on Google for 'しめる　とじる　違い' I liked this page the best http://nihongo24.blog.fc2.com/blog-entry-8.html

Edit:
In answer to your post before this one, you can say 本を開く【ひらく】 so perhaps your missing word is あく?

So basically, the difference between shimeru/tojiru and shimaru is that we have multiple objects with shimaru (like with ageru, ireru and dasu. Something ~is done~ with an object) and only single ones with the others (like noboru, hairu, deru). And I'll just have to learn the individual differences between shimeru/tojiru and akeru/hiraku
(pardon the rōmaji, I got lazy)

開く（ひらく） is different; in the example you gave ("本を開く"), 開く is read as ひらく, which expresses the idea of spreading something open. ひらく can be transitive or intransitive, depending on the sentence, so it can be something a subject does, or something that is done to an object.

I just looked this up (I never really thought about it much), so hopefully one of the more advanced members can weigh in on this.

EDIT: Should really refresh the page after searching...

I think I've got it guys, ty!
What I have right now:
あける: something opens. Instead of "something is opened" think of this as the object doing it "on its own". The store opens at 9 o' clock, etc.
あく: someone opens something. I open the door, I open the window, etc.
ひらく: this can be both "something opens" and "someone opens something" but the main difference is that there is a spreading movement with this. Like a flower unfolding, or someone opening a book.

You've got あける and あく backwards. By the way, there are a lot of verb pairs like this (transitive/intransitive) in Japanese.