Igor here is the process for me:
1) Tell your hotel your dates of arrival in Kuwait and tell them that you need a visa. It's important to do this in advance as in my experience it takes 5-7 working days for the visa to be processed. Make sure you let them know you're coming by sea.
2) The hotel will be your sponsor and apply for your visa - they'll need your passport copy as a minimum, and if I'm not wrong, a copy of the highest education degree received by you.
As I said, it should not cost more than 5 KD, the condition being you'll have to stay at the hotel that is sponsoring you (that's the benefit they get out of the whole thing). In my case, the visa charges are included in my hotel bill.
3) The hotel should mail you a scanned copy of your visa, once approved. It will be in Arabic, the only thing to check if your name and passport details are correct.
4) Now here's the catch - while coming by air, my hotel drops off the visa at the airport. I already have a printout of the scanned copy, and just before immigration there is a counter where I show them the printout of the visa, and I get the physical copy of the real visa. I'm not sure if this will work if you're coming in by sea, or if this is even an option at the seaport.
Good luck, I hope this helped a little.