A Google account will help you effectively use all the Google products like Gmail, YouTube, Google plus, Google Maps, Android and other products from Google.
You will be able to use one Google account to sign in to all Google products if you want to. Google however, allows users to have more than one account for most of their products (except Adsense) if you wish to separate your activities.
To create a Google account, all you need is to fill in the sign up form and submit. You will have a fully functional Google account immediately.
Ensure that the information you give in your account is as accurate as possible. The username in particular cannot be changed in future. The username will be part of your email address if you use Gmail.
Make sure your password is strong and cannot be guessed easily. The mobile phone number and alternate email address are important because they will be used to recover your account in case your forget your password or your account has been hacked.