Windurst can take the Zulkheim Region (Valkurm Dunes, Konschtat Highlands, La Theine Plateau, etc.) through extensive Expeditionary Force missions or by arranging it with the other nations on the server in an effort to get everyone to hand it over for one week, as was done on Seraph with the Ronfaure-Gustaberg-Sarutabaruta trade two years ago.
Apart from that there are several ways to take over Zulkheim region for the week. Having lot of players from Windy gaining experience points there, either solo or in party, is the primary way. There is also Garrison Ops, the resupply quest (for a small amount of regional influence), and trading unused equipment or evoliths to the outpost warp npc. Bear in mind these must obviously be done by Windurstians. These also apply to any other region in conquest.