When you first signed up for your Gmail account, you had to pick a password, which will remain the same until and unless you manually change it yourself. It is not only possible to change your password, but it is in fact safer to regularly change your password (in case someone got hold of it, your changing your account's password means that this person will no longer be able to login to your Gmail account). As you'll see in this tutorial, changing your Gmail password only takes a minute!
The first thing to remember is that when you created your Gmail account, you actually signed up for a "Google profile", which allows you to sign in to all kinds of services with the same user name and password (this includes all the Google services (like Google Analytics, Google Search...) as well as other Google "properties", like YouTube).



This is literally all it takes to change your Gmail password; and while it took you a bit longer since you were following this tutorial at the same time, it is very quick to change once you know how to go about it! A later tutorial will focus on the password recovery process itself.
Caution: changing your Gmail password affects your "Google profile". So you will need to start using the new password for all services that use your Google account for authentication; this includes all services belonging to Google (or that use Google for login), like YouTube.