By default, when you sign in your Gmail account, you will see Hangouts at the left-bottom corner. If you do not like the chat window on the left, you can bring it to the right side. Please see below for details.
Step 1: Login your Gmail account (please refer here to open one if you do not have an account yet);
Step 2: In the Gmail account, click the "Setting" button from the right-top corner;
Step 3: Click the "Settings" command from the drop-down list;
Step 4: Click the "Advanced" tab in the settings menu and check "Enable" in the "Right-side chat" section;
Step 5: Click the "Save Changes" at the bottom;
Step 6: The chat window is now on the right.
If you want to turn off the chat, please see here for details.