Summarize:

Tap the Google Chrome app icon, which resembles a red, yellow, green, and blue ball. It's in the bottom-right corner of the screen. A menu will appear. On Android, you'll instead tap ⋮ in the top-right corner of the screen. Tapping it prompts a drop-down menu. This is in the menu. Doing so opens the Settings page. You'll find it at the top of the page. If you instead see your name and the email address you want to use at the top of the page, you're signed into Chrome. You can check your Sync settings by skipping ahead to the last step in this method. Tap once the email address with which you want to use Google Chrome. If you don't have an email address listed here, enter the email address and password for the account you want to use when prompted. This is at the bottom of the screen. Skip this step if you had to sign into your Google Account manually. It's a blue button in the bottom-right corner of the screen. This will sign you into Google Chrome. You can ensure that sync is enabled for all of your Google Chrome activity on your current mobile item by doing the following:  Tap ⋯ (iPhone) or ⋮ (Android). Tap Settings in the menu. Tap your name and email at the top of the page. Tap Sync near the top of the page. Tap the white "Sync everything" switch (if the switch is blue, Google Chrome Sync is enabled).
Open  Google Chrome. Tap ⋯. Tap Settings. Tap Sign in to Chrome. Select an email address. Tap CONTINUE. Tap OK, GOT IT. Turn on Google Chrome Sync if necessary.