In high school your teacher probably wasn't too picky about whether you used parentheses or commas to set apart ideas within a sentence. However, if you're in college and you want to impress your professor or you're in the real world trying to get something published, a well-used pair of em dashes can really set you apart.
An em dash used in place of a comma can make things easier on your reader. This is especially true if there are already a few commas in the sentence. An em dash will draw the reader's attention, so make sure to use it only when you want to really want to put emphasis on an idea.
An em dash used in place of parentheses will make the set apart information really pop. Also remember, if you are replacing a parenthetical with an em dash at the end of a sentence, you only need the one em dash at the beginning of the parenthetical idea.
Make sure to use the em dash sparingly. Rarely should it be used more than twice in a sentence. If you have more than two em dashes your reader will probably just end up confused rather than impressed. It is also important to note that em dashes are considered less formal, so keep your audience in mind (i.e. if this is a research paper, maybe you don't need to be so flashy).
Word will automatically make an em dash for you if you type a normal dash with spaces before and after it. In most cases, it is proper grammar to have no spaces between the em dash and the words it separates, so after word automatically creates the em dash you should delete those spaces.
You should also check out Slate's article against em dashes to get a perspective from the other side of the aisle.