Launch Chrome and open the main menu (tap the three-dots icon on the toolbar), then tap Settings. Assuming your device’s copy of Chrome has not already been attached to a Google account, you should see a grey bar labelled ‘Sign into Chrome’ at the bottom of the screen. Tapping this bar will bring up a list of all the Google accounts you’ve already signed into on your device (eg for multiple Gmail accounts).
Select the account you wish to sync with. Return to the Settings menu and you’ll see the same Gmail address at the top of the menu; tapping this will take you into a new screen where you can select the items that Chrome will synchronise, eg autofill profiles, bookmarks and open tabs. If you set up a passphrase on your desktop browser, you’ll see some red text beneath the Encryption option at the bottom of the screen. Tap this and enter the passphrase. Then, Chrome will download all of your browsing data from Google.