Welcome to Riga, my dear friend! Let me tell you where you are if your destination was chosed to be Riga.
You arrived by airlpane? So, you are at the Riga airport, approximately 10 km from the city centre. So I guess, you have to get to the city centre. Behind the car park in front of the airport building you will see the bus stop. You can always take bus Nr. 22 – which will take you to the centre and back to the airport. You can buy the ticket from them bus driver and it will cost you 0.70Ls. There is also an airport shuttle bus service. These green minibuses stop at different hotels in the city. It will cost you 3Ls (5 Eur). Maybe taxi? Your 15 min drive to the city centre should cost you not more than 10Ls. Trust green Baltic Taxi cabs, haven’t heard about any problems with them and they have fixed price of 9Ls (12 Eur).
Arriving by train? Cool, you are already at the city centre, just few steps from Old Town. By the way in Riga international trains arrive only from Russia. Arrived by bus? No problem, the bus station is close to the train station what means that you are at the centre and few steps from the Old Town.
Ok, by ferry you come from Stocholm and arrive at the Riga passenger terminal – around 1km from the Old Town. Directly opposite the terminal is the tram stop. You can chose trams nr. 5, 7 or 9. Ticket from the driver – 0.70Ls. Of course you will aslo find there taxis, but actually – the distance is not so big, so you can easily walk it starting to enjoy the beauty of the city, if you don’t have a lot of luggage.
If you wanna come by car I’m glad to inform you that Latvia is in Schengen zone – no more time wasting on the border. But if you cross the border from Russia or Belarus you still might need some patience.