All you have to do is to click the download button on the application's Software Informer page, download the installer on your PC and run it. Since PowerDVD10 can only be installed on a Lenovo system, the tool doesn't cost anything.
In case you can't install the program, there are many other solutions that you can use to play DVDs and that won't cost you a thing: I recommend installing VLC media player as it's one of the best tools out there, but you could also try GOM Player or MPC-HC.
If you really want to install Lenovo PowerDVD10 and you run into the "This application can only be installed on a Lenovo system" error, there's a workaround, but it takes a lot of effort. Press Win + R on your keyboard, type msinfo32 in the Run box that pops up and hit Enter. In the window that opens up, look for the System Manufacturer filed and copy the manufacturer's name, exactly as it's written there.
For the next step, you will need to install a tool like 7-zip or WinRAR, and manually unpack the installer file that you downloaded. Now, go to the folder where you unpacked the files, look for one called custom.ini and open it. Inside the .ini file, look for the line: CLScan=LEGEND Dragon (near the bottom of the page) and change "LEGEND Dragon" into the manufacturer that you've copied from the System Information window. (It's case sensitive so you need to write it exactly the same.) Finally, save the text file, then run Setup.exe from the unpacked folder and the installer will now work.