How do I try and run code that I have written in ACE Cloud 9?
You could possibly make a temporary file in your system, and in an iframe, open the file.

Important Note
This could be insecure as they could get the URL and execute code to delete ../../../ or something, which could harm your files.
I am using ACE to allow people to code freely on my website. How would I run this code. 
I would like a run button in the bottom left corner (I can do that in css), but how would I run it, as it is python. I have added extra tags, as you can write these languages in the ace editor. When I mean,  a run button, I mean like on codecademy, where you write some code, then it is submitted.