First of all, you get there by flying on a plane. Many russian tourists go to Thailand by entering Beijing airport first then going to Thailand. If you want to visit some nice places visit the palaces the ice palace it's very cold up there and if you really want to see something cool go visit Trenoble lol forgot how to spell it. 

Vladivostok is very easily accessible by train from Beijing.  Take an overnight train to Harbin, or a rapid D train from Beijing to Harbin.  From Harbin, take the train for Vladivostok.  Beijing - Vladivostok by train will be about two days travelling times.  Vladivostok is miserable in the winter unless you avidly like - 35 C. weather.  It is really pleasant late April through late August when the temperature starts to dip again.  If you can read Russian, look here please:

http://polusharie.com/index.php?topic=42122.0

Как попасть из Харбина во Владивосток?

Securing a Russian visa can be a bit of a problem however and you definitely will need an agency.

There are various airlines flying around that region but I wouldn't get on one of their airplanes for love of God or money.  Vladivostok is a city built on hills, with a recently restored 19th century Russian Orthodox cathedral.  It also is home to a good number of (North) Korean refugees.  The harbor is pretty but you cannot take pictures of it at all.  It is also filled with decaying Soviet-era submarines, warships, etc., etc.