Another useful group of words that I learned are used to describe the position of something.
Here are the most common:
上 (Shàng) is up or on
下 (Xià) is below or under
前 (Qián) is in front
后 (Hòu) is behind
旁 (Páng) is beside
里 (Lǐ) is in (like inside)
外 (Wài) is out (like outside)
右 (Yòu) is right
左 (Zuǒ) is left
Often these words are used with either 边 (Biān) or 面 (Miàn) to indicate the position. Both seem to be able to be used interchangeably, but I know most of my Taiwanese friends seem to use 面 (Miàn) most of the time, except they seem to always use 边 (Biān) for left and right.
You'll often hear these after a noun, to indicate a position, in relation to the noun. So
房子后面 (Fángzi hòumiàn) will be "rear of the house".
镜子前面 (Jìngzi qiánmiàn) is "in front of the mirror".
I'll write more soon on the best methods for learning. If you want to get a taste for it in the meantime though, my current favorite site is iTalki, and my favorite teacher by far is Amy He. If you decide to try it, click here and it's cheaper for both you and me.