One thing that I feel international students have the most confusion over is the Formal vs. Informal kind of speaking.  As you may have noticed from the title, Formal and Informal aren't the only levels of honorifics. They are the types that are on the very ends of the spectrum.

So in order from most polite to least polite: Formal, Semi-formal, Polite Informal, and Informal. 

First, and most important, Formal.  This formal honorific is used when you talk to someone like your boss.  Or your parents-in-law.  Or the president.  Someone way upthere. Someone with a high position that you don't know very well.  If you know these people like the back of your hand, you can use semi-formal to them.  But formal is for the very high positioned.

People think formal speaking is just informal speaking with a 요 (yo) at the end.  This is not true (in fact the 요 is mostly used in semi-formal speaking). Formal sentences usually have 입니다 (im-ni-da) 합니다 (ham-ni-da), etc. at the end.  입니다 and 합니다 has a sense of unfamiliarity.  So when you use those, you give an impression of formality and unfamiliarity.

Semi-formal speaking is practically informal speaking with 요 at the end.  This is used to talk to family(grandparents, aunts, uncles, etc.), and possibly anyone you would talk to with formal speaking as long as you are familiar and friendly with them.

Polite Informal speaking and Informal speaking are similar.  Polite Informal Speaking is usually used for friends (or your parents disrespectful-young-people-like-me) that were born before your birth year, and Informal Speaking is for friends that were born in your birth year and younger.  The only difference is that you can't say certain things in Polite Informal, such as 야 (Yah).  Both Informal Speaking can end in a range of endings.  

Hope this helped clear up any confusion/misunderstandings of the Formal vs. Informal Honorifics.  

It could have made it worse but...