You really have two options: public buses and taxi. And feet of course.
Buses are cheap and go almost everywhere in a city. For foreigners it might not be the best option, because there is no single map in English inside buses, most of the bus stops don’t have it’s name written anywhere in English or even in Russian. Also, they only accept cash (there is a card system for local transport, but so few buses have it, that there is no reason to get this card) and might not have change from big bills. You can definitely use buses if you know exactly how your stop looks like. And don’t even think about asking driver for directions, they don’t speak English. Also from 8 to 10 am is a rush hour for most of directions and same thing is from 5 to 7 pm, so buses can be packed. And it’s hard to catch a bus to many directions after 10 pm. Yellow buses (MAN brand) are generally nicer, because they are city’s property. Sometimes they even have working free Wi-Fi and a screen with names of stops. But they don’t go to all directions.
Most important bus stations is Semyonovskaya (Семеновская) and Main Square (Centralnaya Ploschad, Цетральная площадь). They are both located in a city center, many buses to many directions go from there.
You can use maps.google.com to get directions and find bus stops. Most of the times they are correct.
Taxi is cheap. However, there is no some sort of Yellow Cab or other similar taxi system, taxi cars are just random cars, many times they have taxi signs on them and many times they don’t. So to identify your car you need to look at a number plate. It is not easy for a foreigner to call and get a taxi, because nobody speaks English on the other end. Some hotels probably can help, but much easier is to use phone apps or websites.
Most popular is this one: http://taximaxim.ru/en/ you can also get an app. After you order a car, you will receive an automatic call and SMS with a plate number of your car and for how long you will have to wait, you also will see the approximate cost. It can change a little. Mostly drivers will not try to cheat you. Of course, they also don’t speak English and if you have a tricky location they might not know exactly where it is, but almost all of them have navigation system. They also might not have a lot of change and they never accept credit cards, so be prepared. Most of the people use this taxi because it is cheap, comes fast and ok in general. Cars might not be very new though.
Other taxi you can use is more like Uber – it’s Yandex-taxi https://taxi.yandex.ru , but in order to use it like Uber and pay with a card you need to download an app.
And I forgot to tell you, there is no Uber in Vladivostok. I am sorry. Well, actually check on arrival, may be it has appeared.