In general, the steps to resolve are a combination of JS plugins, conditional comments and a testing environment.
I have successfully used respond.js for media query support, you can download it from github.
- use conditional comments to avoid adding this in modern browsers
<!--[if lt IE9]>
<script src="..directory-path/respond.js">
<![endif]-->
Depending on how detailed you want to get with supporting CSS3, you might set up PIE.htc - css3pie.com
Finally, in order to get a better grasp on the problems and results, look into browser testing options:
Set up a VM - https://modern.ie/en-us/virtualization-tools#downloads
- This has been a very successful method for me and I consider it the most reliable method
Browserstack - you can set up a trial account for 30 days; it's a good tool but as before, it's not as reliable as the VM.