By air. Kumasi International Airport (KMS) handles short hops from Accra (about 45 minutes) operated by Africa World Airlines and PassionAir. The flights are cheap by international standards and a sensible choice if you value the time over the cost. The airport sits north of the centre — taxis to Adum take fifteen minutes.
By bus. STC, VIP, and OA run air-conditioned coaches from Accra (roughly five to six hours), Cape Coast, Tamale, and Takoradi. The STC station is in Adum and the VIP terminal on Asafo are both walkable to the city centre. Book a seat the day before during weekends and holidays.
By tro-tro. Cheaper, slower, and considerably less comfortable. Tro-tros leave from various stations around Kejetia for destinations across central Ghana — fine for short hops, less appealing for the long ride from Accra.