Signing in to your Google account with your Google Chrome browser affords you a number of extra features, such as saving and syncing your bookmarks across all the devices you use Chrome on, screen sharing, and easy transfer of pages from your mobile devices to your desktop and vice versa.

Sign in to Chrome

Step 1: Open Google Chrome, and look for your user icon in the top right.

Step 2: Select Turn on Sync.

Step 3: Enter your Google email address, then select Next.

Step 4: Enter your password, then select Next.

Step 5: You'll be asked if you also wish to Sync your bookmarks, search history, and other information across devices.  This can be changed later in settings.  For now, select Yes, I'm in.

You can tell if you are signed in or not by what the icon looks like.