First you'll need to check the compatibility of your Mac with the subsequently released version(s) of macOS. You can refer to the support document from Apple, Use the Mac operating system that came with your Mac, or a compatible newer version. This will help you in determining if your Mac can run macOS High Sierra (if not than what is the latest released supported by your Mac). Specifically, to check if your Mac can run macOS High Sierra, check if your model of Mac is listed under Can your Mac use High Sierra? section in the document, How to download macOS High Sierra.
As mentioned, you are already running OS X Mountain Lion 10.8.5. All the subsequent releases of OS X (later re-branded as macOS starting with macOS Sierra 10.12) are released by Apple free of cost and can be easily downloaded using the Mac App Store available on your Mac.
If you can visit an Apple Retail store, you should be able get assistance with upgradation to the latest supported release for free. If you do not have one in vicinity, you can also check with an authorised Apple retailer and check for the pricing. There are no costs from Apple whatsoever for upgradation (in your case).