Analysis
Waveshining consists of three steps, Shine, Wavedash, and walking towards your opponent. Walking towards your opponent is important, because it allows you to Shine your opponent again.
Getting Used To...
Jumping Out Of Shine
The timing of when you can jump out of Shine changes, depending on if you hit your opponent or not. Getting used to the timing of jumping out of Shine, when you hit your opponent is essential to Waveshining. Once you get used to the timing of jumping out of Shine, you can time your L or R press like a normal Wavedash. I'll provide a method to practice the timing later.
Walking
Waveshining also requires you get used to walking out of Wavedash. Although I don't assume this is difficult. You probably are already used to this anyway.
Practicing
Jumping Out Of Shine
Practicing the timing of jumping out of Shine, while you hit your opponent, is important. For this method, make a second player Bowser and set the rules set to an infinite match. Then set your handicap to 1 and Bowser's to 9. You can also unplug the second player's controller, and plug it in while holding up. You now can keep Shining Bowser, while practicing the timing of jumping out of Shine.
Waveshining
For this method, go into Training Mode and select Captain Falcon as your opponent. Then select Final Destination. This method also works for practicing the timing for jumping out of Shine.
Future Content
I will be editing in options out of Waveshining, in the next few days. I also might be editing the wording of the guide, and adding more descriptions later.