One problem you will have is that the bult-in Tone function of the Arduino can only play one note at a time. The sheet music of the first track shows multiple simultaneous notes. There are ways to play more (third-party libraries, for example) but you have to decide if you need that capability enough to do the extra work. If you want to go with single notes, just take the top one (highest pitch) in each column.
Next step is learning to read music enough to determine the notes and durations. Here is a tutorial that covers the basics: http://datadragon.com/education/reading/
The sheet music link for the second piece gets a "Page Not Found" error. The YouTube link for the second piece sounds like it's mostly a snare drum track which will not reproduce well as notes on an Arduino.