Kaunas is a city in Lithuania.
To Vilnius
When going to Vilnius you take a bus to the highway. There is a bus stop on the highway where it's possible to get rides, but it might also be a good idea to not deal with the hitchhiking competition and place yourself at the entrance of the highway.
Quite far away from Vilnius there is a huge hypermarket next to the highway with a free bus to the centre.
To Poland or Latvia
When going to Poland you take a bus to the end of the route. Make sure you make it to the Polish border. From there you will easily find a long ride.
Alternatively get a bus from the centre to IX Fortas (I think its bus 23 or 29, but I'm not sure, look on the maps at every bus stop) , this is the main road where the motorway to Vilnius joins up with the E67 (Via Baltica north and south) - with a PL sign you should easily get a lift from a truck to the border. Note that this border is *very* slow for trucks to cross and theres always about a 2 hour delay, so when the truck stops, get out and walk (or try to hitch a normal car) to the border, just after the polish side theres plenty of room for anyone to stop.