How do I add a new Page template?

I have Touchfolio theme installed and am using a tile plug in called “WP Tiles” you can see what it looks like by clicking the link at the end of this post.

What I’d like to do is keep the sidebar and extend the tiles to (responsively) fill the rest of the page – ie the blank space to the right of the tiles.

Would I need to make a new page template for this? And, if I do, how on earth do you do that?

Thanks!

https://www.fotopiaimages.com/grid/