Private cars to Stockholm: gate A
Private cars to Tallinn: gate C
For gate C, drive along Kanavakatu ca. 200 meters past the Katajanokka terminal. 
Seet the map: http://www.hel.fi/port/images/uudetkartat/etelasatama.pdf
Trucks and empty buses: gate B

How to find your way to the Katajanokka terminal (Helsinki)
From Lahti/Porvoo: Take the motorway to Helsinki, then follow the signs leading to the centre (ship symbol) for about 1.5 km. Turn right (Centre: Keskusta) and follow Varastokatu. After approximately 1.7 km you will reach Sörnäisten rantatie. Continue following the signs leading to the centre. When you reach Pohjoislaituri , take the right lane and follow the signs leading to Katajanokka (ship symbol).
From Tampere/Hämeenlinna: Take Hämeenlinnantie to Helsinki, follow the signs leading to the centre (ship symbol) all the way to the centre on Mannerheimintie. After approximately 5 km you will see a white, round building (Svenska teatern) on your left side just after the Stockmann department store. Turn left (ship symbol) and follow Eteläesplanadi to the Market Square, then follow the signs leading to Katajanokka.
From Pori: When you reach the roundabout in Pitäjänmäki, start following the signs to the centre. After approximately 1 km you will come to Mannerheimintie. From here follow the same instructions as above (from Tampere).
From Turku: Take the motorway to Helsinki and then follow the signs leading to the centre (ship symbol). When you reach Mannerheimintie after about 2.5 km, follow the same instructions as above (from Tampere).
From Hanko: Take the motorway to Helsinki and then follow the signs leading to the centre (ship symbol). Drive by the harbour and turn left into a tunnel on Uudenmaankatu. When you reach the end of Uudenmaankatu curve left and you will see  a white, round building (Svenska teatern) in front of you.  Turn right (ship symbol) and take Eteläesplanadi all the way to the Market Square, then follow the signs leading to the Katajanokka terminal.