You will be hard pressed to find a clear example that the series is about the present world in a literal way. However, the power of a dystopian novel is that it has many resonances with our modern world. So, the best way to make your point about the Hunger Games being about our day and age is to make parallels, of which there are many.
The three most powerful parallels are as follows.
First, in the book there are districts, which focus on one or two trades. This division of society is something we have today. Certain neighborhoods are known for a trade or a type of culture or a type of person and others are known for something different. This lack of unity and division is a problem of our world.
Second and more pointedly, there is a huge divide in our culture when it comes to wealth. For example, just think about the Occupy Wall Street movement. The 1% control pretty much the whole world. The wealth gap is obnoxious.
Third, there is an infatuation and craze with celebrity culture in the books. This is very similar to our world today.
So, if we start with these parallels, the series is a commentary about our world.