Seyðisfjörður is a city in East Iceland.
There is a weekly ferry run by Smyril line, tel +354 472 1111 - to Denmark and the Faroe Islands. The schedule is complicated but it generally departs once per week at 8AM during the summer half the year (April-June and August-October) , and at 1PM during high season (June-August). Check website for details. Due to the limited market, and rough conditions, prices are very high. A return journey to Denmark for instance will set you back €280-590 with a car or €120-250 per passenger, depending on the season, excluding a supplement fare for a cabin or bed.
The nearest Airport in Egilsstaðir, about 30 minutes away, has regular flights to the capital, there is a daily bus to Seyðisfjörður connecting with the flights stopping in central Egilsstaðir on route. From central Egilsstaðir there are one or two additional departures per day during the summer, as well as the option to change to several bus lines connecting to other parts of Iceland. The buses are run by Ferðaþjónusta Austurlands (tel.: 472 1515) which has no website, but the city administration website  maintains a an updated schedule.