I've declared independence, and one shipload of soldiers came to fight, I defeated them and sunk their ship and since then nothing, How can I progress the war?

Assuming you havent bugged out in some way... They will simply continue sending ships loaded with troops at your cities. You can check the progress with the Independence War report. It will show how many things they have left to send. Usually it will be several turns worth of waves. In addition, if they conquered any of your cities you have to take them back. After that the King will propose peace and grant independence. Game Over.