How to automatically update the Noda Time database, and how often?

How frequently I need to update timezone database.

When it changes :)

You can find this out by fetching http://nodatime.org/tzdb/latest.txt which always contains the URL of the latest .nzd file.

Or if you don't need automation, subscribe to the tz-announce@iana.org mailing list (via the IANA time zone home page) - that contains an announcement for each release.

What are the steps to automatically update the timezone database.

Download the latest .nzd file, then create a TzdbDataSource from it, as documented in the user guide:

IDateTimeZoneProvider provider;
using (var stream = File.OpenRead(...))
{
    var source = TzdbDateTimeZoneSource.FromStream(stream);
    provider = new DateTimeZoneCache(source);
}

That's assuming you're happy to wait for me to build the nzd file and upload it, of course. Alternatively, you can fetch the latest source code, build the NodaTime-All solution and then run the NodaTime.TzdbCompiler utility yourself. This is easier now than it used to be, as you can just specify a URL to the latest .tar.gz file and the directory containing the CLDR files.

There isn't a simple way of updating NodaTime.dll itself to embed a new version of the tz database - basically it comes with whatever was current when it was built, and if you want something more recent you need to use the code above.