The first step to playing this intriguing game is to setup the board correctly. Chess boards are of many types. As a kid you might remember playing on those glass ones, but the best ones are usually wooden or roll up chess boards. These are the ones you would find in professional tournaments as well.
So now, let’s assume you have a chess board in front of you. Which side of the board should face you?
The first thing to take care is that you should have a white(light) square on the bottom right and the top left corners.
The top left and bottom right squares need to be light squares.

Once the board is placed correctly, the pawns will be placed on the second horizontal line of squares as well as the second last horizontal line from you.
So now, which coloured pieces will you take, White or Black? White moves first and thus has a slight advantage at the start which slowly diminishes with more and more moves being played. However, to keep the game fair, alternate between White and Black each game. The colours for the first game can be chosen by a coin toss.

These are the lines along which you need to place your pawns. The colour you choose will be placed closer to you.

Let’s say that you won the toss and chose the White pieces. Your pawns will be placed like this.
The notations of a,b,…h and 1,2,…8 you see basically are used to identify each square on the board. They are only useful if you are trying to record a game of chess to replay later. To just play however, you only need to make sure that the right bottom corner square is light square.
Now you will place the rooks on the four corners of the board, just like shown below.
Rooks will take the corner squares of the board.

Next, place the knights adjacent to the rooks.

Place the Bishops adjacent to the knights.

You now have only two squares remaining for each colour. Place your Queen on the same coloured square as the colour of your pieces. The White queen goes on a White square, the Black queen on a Black Square.

The last remaining square goes to the kings et Voila! the chess board is set up.

Below you will find the same schematic way of setting up the pieces from Black’s side, just so that you don’t get confused.

Pawns

Rooks

Knights

Bishops

Queens

Kings