How does the Russian Federation enforce the blocking of websites for end users? I know that ISPs have a database of DNS records that will redirect the user to a corresponding IP address for a given URL. Does that mean that every ISP in Russia has the same DNS and the records are always up-to-date?
The process of Russian Federation enforcing it's filtering of websites for access is by handing down the list of IPs that should be blocked to the Internet Providers that operate within it's borders. How exactly the providers will do that, is entirely their decision, as long as the result is that website is unavailable for access to users trying to access the said websites through ISPs located within Russian Federation.
The Russian Federation maintains a list of blocked websites, known as the Internet blacklist, the contents of which are decided upon by the Roskomnadzor and the Federal Drug Control Service of Russia. Russian Internet Service Providers are compelled to block these websites.
On a technical level, there are many ways an ISP could a block website, and they likely don't all pick the same solution, so it is unlikely that there is one simply answer. To answer your question regarding DNS however - what you are referring to, a database of DNS records, is called a DNS server, sometimes called a name server. Simply put, DNS servers can negotiate in a hierarchical fashion to determine the truth about what the record set is. This is how name records are standardized globally, not just inside the Russian Federation.