While you can access Google Drive from your Gmail using the apps icon, the easiest way is to simply type in drive.google.com into the search box.
The address for the new Google Drive is the same.
Control T (Command T on a Mac) will open a new tab. Your cursor should be in the addresses bar. You do not need http:// or www. You are wanting to go to Drive, so just start typing drive. You will need to add the .google.com as well. You may notice that many Google products follow this pattern. books.google.com, scholar.google.com maps.google.com, etc…