By plane

Pint-sized Tokushima Airport, to the north of the city, has daily services to Tokyo, Nagoya, Fukuoka and Sapporo. Buses to JR Tokushima Station take 25 minutes and cost ¥430. The schedules are synchronized to flight departures/arrivals.
Buses run to the station from Kobe Airport every 1-2 hours at 55 minutes past (2 1/2 hours, ¥3200). Airport Limousine buses operate from the nearest international gateway, Kansai International Airport in Osaka (2 3/4 hours, ¥4000 — cheaper if you purchase a round trip ticket).

By train

From Okayama, take a Marine Liner rapid train to Takamatsu, then transfer to the Uzushio limited express for the run to Tokushima (2 hours, ¥4420). Two daily Uzushio trains run directly from Okayama, leaving at 11:05 and 19:05, with no change of trains required (¥5050).
The JR Tokushima Line runs toward Ikeda (2 hours), for connections south towards the Iya Valley.

By bus

If arriving from Kansai via Awaji Island, you're pretty much guaranteed to end up in Tokushima. JR Bus operates many services to Tokushima: Awa Express bus service leaves from Kobe and Kobe Airport (2 hours from Shin-Kobe station, ¥3200, 15 daily round-trips), Osaka (2 3/4 hours, ¥3600, 23 daily round-trips), Kyoto (3 hours, ¥4100, 7 daily round-trips), and on weekends and holidays, Nara (4 hours, ¥3900, 2 round-trips). Keihan Railways has its own highway bus that travels to and from Kyoto and Hirakata.
The overnight Dream Tokushima bus runs from Tokyo and Shinjuku (10 hours, ¥10000 each way).

By ferry

Ocean East operates a ferry service between Tokyo, Tokushima and Kitakyushu. Both the Tokyo and Kitakyushu runs are overnight; passengers can book Western-style bedrooms, bunks, or sleep on the floor. If you're sleeping on the floor, this is one of the cheapest ways to get to Tokushima Tokyo fares are ¥9310 each way, and Kitakyushu fares are ¥6790 each way. First-class tickets are ¥25,480 on the Tokyo run and ¥17,920 on the Kitakyushu run.