1) Buy Onnibus ticket Vantaa → Tampere
In the airport go to HLS trains Here is the semi-ring road of local trains
Take the I train and go to Kivisto. It takes less than two minutes.
When you are at Kivisto walk to Keimolanportti bus stop which is near the restaurant and wait for Onnibus.
To see photos of this road - read the manual below
Buy Onnibus ticket from Tampere to Vantaa.
Get into the Onnibus which is on Tampere - Helskinki route. You can do it e.g. in Hervanta near DUO
Leave the bus at Keimola-Vantaa station.
You are at Keimola around 20:00. Follow the direction pointed by the green arrow.
Go downstairs to a tunnel and turn left.
Walk approximately 250 meters to the Kivisto railway station.
Here is a photo of the tunnel (picture captured at 21.10.2016)
When you see this stairs go upstrairs (follow the green arrows).
The blue arrow is pointing to the Kivisto railway station.
Enter the station and go downstairs to the trains.
If you were entering the station same way I did then you need the left track. Anyway, it is better to doublecheck it. You need the train to the airport (Lentoasema) which leaves at 20:10
If you are late for this train you can take the next one at 20:25 and still be in time It is a ring road but it will take much more time to reach the airport in opposite direction.
Go to the airport (Lentoasema) station - it is the second stop and it takes approximately 10 minutes to be there.