The hanse or hansa dominated the trade through a combination of merchant guild alliances, privateering, toll-exemption and imperial protection.
The most important factor was the League system itself. The hanseatic league grew from a collection of (Low German) Merchant guilds that banded together to maximise their individual assets and provide market access to each other. Just as in our time, shipping was the most cost effective long range method of transport. Because of this rivers were vital for trade. Many of the Hanse cities controled imporant rivers mouths that provided access to productive hinterlands.
Together the members of the League controlled sea and river access to modern day North Germany, Sweden, Russia, Finland, the Baltic States, Poland and parts of the lowlands and the rhineland. Additionally they controlled fishing in the north sea and the baltic sea. This access provided them with the long range trade monopoly in the baltic sea. The importance of this alliance system cannot be overstated as it allowed the League to bully and block various other powers allowing the League to demand special trade privileges in Flanders, France, England, Novgorod(Russia) and Poland.
The monopoly on the seas themselves was maintained through privateering (Legal piracy) and commerce raiding. The Hanse primaraly fought wars with other merchant groups such as the Hollander/Zeeuw merchants and the English merchants. In these wars both sides engaged in hijacking each others merchant ships, trying to disrupt trade until the other side gave up. The English lost their war with the League, but the Dutch managed to break through and gained access to the polish grain trade.