My store is really slow, so I decided to install Varnish, but it's really complicated for me. I successfully installed Varnish on my CentOS, created VCLs and installed turpentine varnish plugin for magento. Still, I don't see any progress, my site is still quite slow. I have checked the headers and varnish is on. My other websites that uses cache (on wordpress) are extremely fast now.
So your job would be find a problem why varnish cache is not working good on magento and fix it. The final goal is to speed up the store.