To back up your files manually:
Plug your external drive in, go to 'Computer' (from the 'Start' button) and double click on the icon for that drive. If you're happy to place files straight onto the disk, rather than sorted into folders, that's all you need to do with that drive. However if you'd rather create a folder called, say, 'backup01-01-14', click on 'Organise', then on New Folder. Name your folder and double-click on it to open it. (I'd strongly recommed creating a new folder).
OK. so far you've got just one window open which either shows the 'root directory' (i.e. the whole of the disk) or a folder within it. That window needs to occupy just a part of your screen. (If it fills the whole screen, make it smaller).
Now go to 'Computer' again and double-click on the icon for your internal hard drive. Doube-click on 'Users' and then on your username for your laptop. You'll now have two windows open side by side. (Again, if the window is too big, resize it so that you can see both windows). Click-and-drag any folders you want to back up, to pull them across from the second window to the first one. (The most obvious folders are 'Documents', 'Pictures', 'Music' and 'Video' but there might be others that you want as well). Job done.
To use Vista's automatic backups facility:
Plug in your external drive.
Go to Start > All Programs > Accessories > System Tools > Backup Status and Configuration. Click on 'Automatic File Backup' and follow the prompts.