There is an airport in Vitoria but there are not much flights there. You can find more international cheap flights to Bilbao or to Madrid. Once there, you can easily come to Vitoria by bus. (see the intructions of coming to Vitoria-Gasteiz by bus )

VITORIA-GASTEIZ    AIRPORT

Airport of Vitoria (Foronda)  www.aena.es
The airport is about 11 km. away from the city. There is a bus from Airtport-Train Station-Bus Station which departure time depends on the arrivals of the flights. It is about 25 minutes and 3 euros.

The only operating company is Air Nostrum and have flights from Madrid and Barcelona.

BILBAO AIRPORT

Bilbao Airport lies 12 kilometres away from the city of Bilbao which is 66 km away from Vitoria-Gasteiz.

Companies and citys with flights to Bilbao:

BUS FROM BILBAO AIRPORT

The bus that links Bilbao and the airport is Bizkaibus A3247, a yellow urban bus whose departure point is Termibús.
At the airport, the departure point is the stop in front of the Arrivals Terminal, and ends its route at the Termibús.
The buses to Vitoria-Gasteiz have their departure point at Termibus. The operating company is LA UNION, there is a bus nearly every our and it's about 5 euros. 

MADRID AIRPORT

The Airport of Madrid is the biggest and more international airport of Spain. Probably, you will find a direct connection from your nearest airport.

BUS FROM MADRID AIRPORT

There is a daily bus from Madrid-Barajas to Irun that stops in Vitoria (runned by Alsa/Continental Auto). It departs at 6:15 and arrives at 11:30.  (see www.alsa.es ). Alternatively, you can go from the airport to Madrid by metro and then from Madrid to Vitoria by bus. Maybe cheaper.
At Madrid-Barajas airport take the metro (about 2 euros) line 8 direction Nuevos Ministerios. At MAR DE CRISTAL change to line 4 direction Argüelles, stop at the AV(ENI)DA DE AMERICA.
At the Avenida America Bus Station, go up to the 1st stage (Largo Recorrido). The bus to Vitoria is runned by Continental-Auto. It is 24 or 37 euros, depending on the bus. (see www.alsa.es )