You can fly directly to Vaasa Airport which is located around 15km from the city centre. A taxi from their cost about 20 euros. The Vaasa Airport is operated by SAS, Blue1 and Finn air. 14 planes land at Vaasa airport on weekdays.
The train station is located 300 meters from the market square and it is quite convenient to use. It cost around 30 euro from Helsinki to Vaasa depending on the train type. If you come from Helsinki, you must change train twice, in Tampere and Seinäjoki. Eight daily return trains between Vaasa and Helsinki. Check out VR, national railway.
The Bus station is located in the same premises than train station so it is also near the city centre. Buses take longer but cover more cities they usually are to be used if one comes from a city that has no train station. See also Matkahuolto, a Finnish bus company.
RG Line operates between Vaasa and Umeå and it takes four hours. Check out RG