If you're going to try things yourself, you can probably forget about backing up your files for now anyway. You need to get hold of a proper recovery drive (on a USB memory stick) for your version of Windows. So which version is it? (Windows 7, 8, 8.1, 10?). You might also need to know whether you've got a 32-bit or 64-bit version of Windows. (If you don't know, please provide the make and model of your laptop from the sticker on the bottom).
What you'll need to buy will be one of these:
http://tinyurl.com/lucagjj
(I've not suggested a particular one as I don't yet know which version of Windows you've got).
Then you'll need to ensure that your laptop is configured to look for a USB boot drive before examining the hard drive for a boot sector. To do so you need to get into its BIOS. You do that by pressing the relevant key during its boot-up process. (i.e. before Windows has loaded). There's usually an on-screen prompt to tell you which key to press. Once into the BIOS, you navigate around by using the arrow keys, together with 'Enter' and 'Esc'. It's usually not too difficult to find the settings which determine the boot order.
Then you power down your laptop (by removing the battery, and then replacing it, if necessary), plug your recovery drive into a USB port and boot up. You should then be provided with an option to repair Windows.
If you'd still rather back up your files first (by removing the hard drive and inserting it into a USB caddy) you need one of these:
http://tinyurl.com/mcw84ls
You simply remove the laptop's hard drive by undoing a couple of screws in the bay underneath it (using the watchmaker's type of screwdrivers which any pound shop can sell you a set of) and sliding it out. You then just slot it into the caddy and connect it to your PC via the supplied cable. You'll be able to see many of the files on the hard drive but not your personal ones. To do so, you need to 'take ownership' of the drive:
http://www.techfleece.com/2011/05/15/how-to-take-ownership-of-files-or-folders-or-an-entire-hard-drive/