On your flight to Thailand, you will get an arrival card that you must complete and hand over with your passport to the immigration at arrival. The arrival card is in two parts, one part is for entry and this part the immigration officer will keep. The second part will get an entry stamp, and you get that part back together with your passport.
Take care of the arrival card, as you will have to hand it over to immigration when you are leaving Thailand. You may also have to present it together with your passport while you are in Thailand. Usually, immigration will staple it into your passport.
You must fill out the arrival card with information about your name, date of birth, nationality, passport number, flight number, etc.
You will also need to disclose your address in Thailand. You do not have to write down the name and address of your hotel, the name of the city will usually do fine. If you are travelling around in Thailand, just type the name of the first city you visit.
You must also state your occupation, and what city you live in. Please note that you must write nationality, occupation and city names in English (Thai is also acceptable). You can see all the fields of the form in the image below; click it for a larger version. The article continues below the image.
If you arrive at the immigration desk without a filled out arrival card, you will be rejected and you must then return and get an arrival card from the staff at the airport. After filling it out, you will have to re-queue. Please note that the queues can be very long and it is not fun to stand in line for up to an hour, only to have the immigration officer reject you. That is probably not the best way to start your holiday.
Therefore, I will recommend that you complete the arrival card on the plane. If you do not automatically receive an arrival card from the staff, then ask for one. If you did not bring a pen, you can probably borrow one from another passenger or from the staff.
Should you lose the arrival card during your stay in Thailand, you will be able to get a new one at the airport on departure. However, you do risk trouble, depending on the mood of the immigration officer, as you do not have the original with the arrival stamp.
In some cases, it may be necessary to obtain a new arrival card before you go home. If so, you can get one at the local immigration office at your destination. Normally, ordinary tourists do not need the arrival card during their stay, but you will need a new one if you need a work permit, if you want to buy a scooter, or if you otherwise are dealing with the authorities.