You say this expression when you want to compliment someone on a job well done. This phrase is similar to "good job" or "excellent." So when someone gets an A on an exam, you say, "Way to go! That's awesome." This phrase only works when you talk to someone, so don't use it in the third person, when you're talking about the excellent job someone has done.
A: Hey Tim! I heard you got a 110 on the TOEFL. Way to go, man!
B: Yeah, thanks. It was my second time taking it. After the first time, I knew what to expect, so it was a little easier.
A: That's awesome. What was your score the first time?
B: I got a 98 the first time. What about you? What have you been up to?
A: Oh, I just got accepted to grad school. I start school this fall.
B: Yeah? That's great. Where are you going?
B: Awesome. That's where you wanted to go, right?
A: Yeah. Columbia was my first choice.
B: Way to go, man.
What have you been up to? - What's new? What's the latest?
Alright. This is a fairly easy expression to use, so do your best to say it today. Tell someone they did a good job. But instead of saying "good job" or "excellent", say way to go!