You do that with divs. First, you have a div where you put the existing slideshow and then next to it you put another div and embed the video into it. The two divs have to be part of another div that is the same width as div 1 + div 2 in order for them to be side by side.
in your html:
<div class="div1and2"><div class="div1">
dino slideshow </div>
in your css file:
Videos are started with the < embed src="url" > code. By the way, youtube videos already have copy and paste codes on their websites.