Open chrome and left click on the tab as shown below. Chrome can be downloaded from here.
Enter your email address and left click next. If you don't have a Gmail account, use the Create an account link as shown in the picture below.
Enter your password and left click Sign in.
Left click the icon in the top right corner and choose settings as shown below.
Left click on Advanced sync settings as shown below.
A new windows will be presented from which you will ensure the Sync everything option is selected. Left click OK.
Once you have completed these steps your current Chrome bookmarks will be sync'd with your Gmail account. You will then be able to use these steps to login to another device, PC or mobile, and have the same access from this new device.