Need help embellishing accompaniments to vocal songs from simple chords

[willyoulaugh]

I have to accompany myself or sometimes others while they sing songs. Often times, all I am given are a few chord letters in a certain order.
So far, I have just been playing the chords in root position or an inversion while they sing and then switch to the next chord when its time. Ive tried mixing it up a little by changing the rhythm or adding random notes on the keyboard and surprisingly it sometimes works (or removing notes from the chord).
However, still this seems rather amateur and simple at best. I am used to just playing sheet music so Im kind of stumped here. I know there must be ways to make this better. Any help? I tried googling and searching online to no avail.
I found a good example online:

I would like to be able to do what she does and better. I tried figuring out what shes doing but then she loses me at times. I think for the most part she seems to be doing some kind of octave thing with both hands... and at the end she adds some stuff to end the phrase...?

And this one:

&feature=related

She completely loses me..... this accompaniment definitely goes way beyond simply chords at times... help?