You can reach Aukstojas Hill by firstly reaching the Capital of Lithuania, Vilnius. Vilnius can be reached very easily by plane, train or car, dependant on where you are coming from. If you are leaving from the UK, you can fly directly into Vilnius and land at Vilnius Airport. Once there, you can either decide to spend the night in Vilnius or head straight to Aukstojas Hill.
From Vilnius, you can reach the peak most easily by car, which is only a 40 minute drive away. If you would prefer to take public transport, you can take the 211 bus line until you reach the stop 3-ieji Medininkai. You will then be able to walk to the peak.