"Aber du siehst es doch!"
It's almost like a "vocal interference" in English. You know how some people take to using "like" too much in a sentence?
"It's just, like, you know..."
"Doch" is a very nebulous word. Don't fret over it too much. It doesn't drastically change the meaning of sentences it is used within. At least not in any context that I can think of. (Someone feel free to correct me if they can think of an example that proves me wrong.)
When in doubt, omit "doch" when translating the sentence. Then just think of "doch" as a reinforcer to whatever the rest of the sentence means.
Now, to confuse things slightly, when doch is used as a reply to something someone else has said, it is meant as polite disagreement.
"It's a beautiful day to go to the beach!"
"Doch! It's raining!"
I'm having a lot of trouble with doch. I get very confused on what it means depending where it's placed. Does anybody have any tips on how I can remember what doch would mean in certain situations?
This word is mostly used for emphasis. It is a very popular phenomenon in German. I'm afraid there is no direct way to learn it. Observe it in different sentences; after some time it will sink in and you'll know how to use it intuitively.
@Naaate This blog post should help clarify some things for you: http://yourdailygerman.wordpress.com/2012/02/27/meaning-of-doch/