Translation:East is that way.
Both mean "over there/over in that direction", however, そちら(formal) or そっち (informal) is used when it is near the person you are speaking to, as in: "over in that direction by you".
あちら (formal) or あっち (informal) is used when it is away from both you and the person you're speaking to. For example, if someone is standing next to you asking for directions and you point down the road directing them to go that way.
"The East" would generally refer to a place rather than a direction. The US is in "the West" (in a world map), Texas is in "the South" (in the US), and so on. I don't think there is a place that's universally referred to as "the East", but a native speaker might infer that you meant either Asia or the eastern US, depending on the context.
I highly recommend www.guidetojapanese.org
It is free and is setup around a language textbook format. You can specifically go to chapters on any of the topics you need. If you go under "Complete Guide", then under "Numbers, amounts, and directions", you'll find a tab for directions. This site is one of the best I've personally come across. Hope it helps. :)