For some reason, I'm having trouble wrapping my brain around these two words. All I know is that they mean "thing" but their usage confuses me. I see them a lot in sentences too (mostly こと). Can anyone break it down for me or provide a link? Thanks.

もの means thing as in object.
こと means thing as in happening or situation.

"Such a thing happened to me too!" would be こと while "I own such a thing as well." would be もの.

Note also that both こと and もの appear in a number of set "grammar" phrases which I think are probably best studied as complete phrases. (eg ~もの(です)か、 ~ものの、~ことはない to pick three randomly). This kind of grammar usage is pretty common, and if you're trying to interpret them as some kind of variant on "thing" you're likely to get confused. Consult your favourite JLPT2-ish level grammar reference :-)

This explanation is from "An introduction to Japanese - Syntax, Grammar and Language" by Michiel Kamermans (which you can download for free from his site http://www.nihongoresources.com/ ):
The noun こと　is used to turn clauses into an abstract thought, rather than the actual thing .... (while) もの　conceptualizes real, but not necessarily tangible, things.
Examples:
こと:
秘密を隠しておけること
"The concept "being able to keep a secret a secret"
いつまでもその秘密を隠しておけること
"The concept "being able to keep that secret a secret forever"

もの:
秘密を隠しておけるもの
"That which is "being able to keep a secret a secret"
or
いつまでもその秘密を隠しておけるもの
"That which is "being able to keep that secret a secret forever"

The concept of being able to keep a secret hidden from the rest of the world is something abstract, while the actual act of being able to keep some secret hidden is concrete. For the abstract idea, こと is used. For the concrete event, もの　is used.