How do I upgrade my operating system?

An "old" MacBook Pro does not help much to identify your model. Go to Apple menu > About this Mac, Year and RAM will determine whether you can upgrade and to which system. This support topic outlines your options even if you can't upgrade to High Sierra:

How to download macOS High Sierra - Apple Support

But your first step would be to install 10.6.8 if your Mac supports it.

Mac OS X 10.6 Snow Leopard - Apple

If you’re running 10.5.8, you buy a Snow Leopard DVD from the link macjack posted, and then update to 10.6.8. A MacBook Pro which originally shipped with Leopard can run El Capitan; one running Leopard can be updated at least as far as 10.6.8.

If you’re running 10.8.5, you download El Capitan or High Sierra from the Mac App Store.

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