Once your upgrade is complete, it's a good idea to clear your site cache. Assuming you've made the leap to concrete5.5 or beyond, all you need to do is visit Dashboard > System & Settings > Cache & Speed Settings > Clear Cache.
This will clear out any outdated pages and other bits of data that might be hanging around.
Upgrading older versions of concrete5
If your version of concrete5 is older than concrete5.4, please read this article: Updating Very Old Sites.
If you run into an unexpected issue or can't figure out what step to take next, try posting to our free Installation forum to get help from the concrete5 community.