Wikitravel has a guide to Trans-Siberian Railway.
The most probable way to get in Ussuriysk is by train either coming from Vladivostok or Khabarovsk. The most impossible opportunity is a trip from North Korea on board of the Soviet steam engine crossing Russian border in Khasan. Buses shuttle between Khabarovsk and Vladivostok twice a day to and fro. Almost every hour a bus departs to Vladivostok and Nakhodka. However they happen to have no air-condition system inside, which is vital in summer. Daily buses to China are equipped with this "must". Bus station Tel.: +7 (4234) 32-22-70
From Ussuriysk, you can take the train to Pogranichny (railway station name: Grodekovo), where there is a daily cross-border train operated by China Railway to Suifenhe. The railway line between Pogranichny (Grodekovo) and Suifenhe uses the Russian gauge, and the journey time is 1hr 30min. The Russian exit border checks take place in Grodekovo railway station before boarding the train to China. Chinese entry border checks take place in Suifenhe railway station after leaving the train. As of 2017, the train (number 401) departs daily from Pogranichny (Grodekovo) at 17:43 (local time, GMT+10) / 10:43 (Moscow time, GMT+3) and arrives in Suifenhe at 17:14 (local time, GMT+8). The return train (number 402) departs daily from Suifenhe at 10:00 (local time, GMT+8) and arrives in Pogranichny at 13:30 (local time, GMT+10) / 06:30 (Moscow time, GMT+3). Check the up-to-date train timetable on the Russian Railways website (note that the railway station in Pogranichny appears on the Russian Railways website as Grodekovo, and Suifenhe appears as Sujfjen'hje). As of 2017, according to the information on the Russian Railways website, a one-way ticket from Pogranichny (Grodekovo) to Suifenhe costs 7.10 Swiss Francs (CHF). As of 2015, a one-way ticket from Suifenhe to Pogranichny (Grodekovo) costs ¥71/person (see this Chinese blog post to view a ticket on this route from 2015).
Remember that the railway station and the city are located in some distance from each other, so use a taxi or a bus going "to the center". The downtown is easy to explore by foot.
In the downtown the historical development is well-preserved as of the end of the XIX - beginning of the XX centuries. So is the Temple Of Holy Lady. The monument of tortoise, a carved bìxì (Chinese: 赑屃), a mix of turtle and dragon can be found in the city's park. Previously such turtles were established on graves of the imperial family of Jurchen (女眞) people in the XII century.
Local brewery OAO 'Ussuriysky Balsam' produces a range of brands from bitters and semi-sweet liquors to cognacs, rums and vodkas flavored with essences extracted from the herbs, berries and sea mollusks of Primorsky Krai. Look for the brand alcohol shops 'Savva Vodochnikov' (Савва Водочников) to buy any of these beverages  or visit a drug-store to acquire medical balsam 'Herbamarin'.