Cross Browser Compatability

I own and operate https://www.UndergroundFlix.com

I have come to realize that after multiple updates and layout adjustments within the past few months that my website is no longer appearing correctly on all browsers. I primarily use Google Chrome when making adjustements so I have not noticed any changes to my page – but I have received several reports that indicate my search page is not displaying correctly in Internet Explorer. How can I figure out what code needs to be changed and what should I change it to? Please help.