Everyone needs a visa to enter Kuwait except for the nationals of other Gulf States. As Kuwait does not issue tourist visas, large hotels can sponsor visas. So you should send a fax of all the relevant information to the hotel (including a fax copy of your actual passport). You will receive a single entry visa valid for one month. You have to then collect your visa from the Kuwait Embassy (who only issue visas against instructions from Kuwait).

To get your visas extended after a month, you have to fly out, get a new visa and return.

If your passport contains an Israeli stamp you will be refused entry to Kuwait.