First, you need to install the Mathematics add-in:

Word (most versions):

http://www.microsoft.com/en-us/download/details.aspx?id=17786

Word 2013:

http://www.microsoft.com/en-us/download/details.aspx?id=36777

After downloading and installing the add-in, you should see additional Tab in your Word:

Pressing on the “Equation” button will open equation editor with many different options and palettes (there is also very convenient shortcut keystroke “Alt- =”):

Make sure that you play enough with this add-in to learn it well. In the homework, you’ll need to write matrices, upper and lower indices, equations, different symbols, Greek letters, etc. If you cannot find some symbol or formula, you could always use hand drawing of any formula by clicking on “Ink Equation”.

For additional information:

https://www.youtube.com/watch?v=VDp2DtQyfik

Another option is to use MathType:

http://www.dessci.com/en/products/mathtype/

This product is much more comprehensive and convenient to use, though it has two main disadvantages. First, it is not free (discounts are available) and only 30-day trial is available. Second, if you want to change the font size in your document, then you need to reopen every typed formula and to change the font size inside the MathType editor.