How to connect Galaxy S2 m250s model via USB?
As you refer to the article utilizing adb backup, you want to use ADB to access your device. So for Windows, you would need to install the corresponding drivers; on Linux, a single line in /etc/udev/rules/50-android.rules will be sufficient.

I'd suggest you read my answer on the question What is ADB..., which (at its end) mentions a few guides to get you started with ADB. For a quick configuration on Linux, follow the steps in my answer on Configuring ADB for Nexus 4 on Ubuntu.

If on the Linux host the device is not turning up in the listing of sudo lsusb, and Windows does not even claim to have found an "unknown device" (as your comments suggest), make sure to rule out the USB cable as a possible troublemaker (try different USB cables; you might even visit a shop to "try before buy", best taking a Laptop with you). In case none of multiple USB cables work, a damaged USB port is becoming the likely cause -- though it might be charging fine, one (or more) of the data pins (or their connections to the board) could be faulty. Which would mean you'd have to turn in your device for service.