Use an iframe to embed your shiny app on another website as follows:
<iframe src="http://shiny.math.uzh.ch/user/doe/shinyapp1/" style="border: 1px solid #AAA; width: 290px; height: 500px"> Your Browser doesn't support iframe </iframe>
With the style part of the command, you can customize the size and look of the frame:
border: set the thickness of the border, the border color as well as the style it should be displayed in (solid, dotted, stripped). You can also deactivate the border completely by writing border: none;
width: set a custom width to the frame. Normally very dependent on the app you load.
height: set a height. Usually you just want the frame to be high enough that no scrollbar appears.
float: You can let the frame float to either the left or right side of the text. If you want two iframes displayed side by side, use float: left on one and float: right on the other.