Before arrival, if you are not a Canadian or Bermudian, you will receive either a white I-94 (if entering with a visa) or green I-94W (if entering on a visa waiver) form to complete. Most persons arriving in the United States under the Visa Waiver Program are no longer issued with I-94W cards, however, as the qualifying paperwork was filled out with the ESTA application.
If you are not a citizen or resident of the United States, you will go through a short interview at immigration, where a Customs and Border Protection officer will try to determine if the purpose of your visit is valid. Just like when obtaining the visa, the most important concern to immigration officials is to determine that you have the funds to support yourself and that you do not intend to work or perform any activity not authorized by the your visa. Be prepared to show proof. If you are on a business visit, have an invitation letter from the company you are visiting, or the registration details of the conference you are attending. If you are a tourist, you may need to demonstrate you have funds available to you. In both cases proof of onward travel may be required. Usually, the determination of admissibility is made in a minute or less, but you may be referred to further questioning in a more private area. At this stage they will likely search your possessions, and may read any documentation, letters or diaries in your possession. Do not bring anything that will imply you will immigrate (employment documents, photographs typically kept at home, excessive luggage, pets). If you are unable to prove or convince the officers that you will potentially abide by the terms of your visa (or visa waiver program if applicable), it can be cancelled on the spot, and you will be refused entry and sent on the next flight home.
Once the CBP officer decides to let you in, you are fingerprinted and a digital photograph is taken. These are additional security measures dubbed U.S.-VISIT that is currently applicable to all non-resident aliens, at a majority of land, sea, and air entry ports.
Like immigration and customs officials everywhere, CBP officials are humorless about any kind of security threat. Even the most flippant joke implying that you pose a threat can result in lengthy interrogation at best, and summary expulsion at worst.
For non-residents, your entry forms will need to state the street address of the location where you will be staying for the first night; this should be arranged in advance. The name of your hotel, hostel, university, etc. is not sufficient; you must provide the street name and number. If it is a hotel, have a reservation under your name. If it is a private address, make sure that the people there know that they are expecting you that day, as officials may phone them and ask them for the name of the guest they are expecting. Make sure you have their contact details (especially phone numbers where they can be reached immediately), and save any text messages or e-mails in which your hosts mention inviting you to stay at their residence.
Once you are admitted, the departure portion of your I-94 or I-94W will be stapled to your passport. Keep it safe as you will need to give it to airline staff upon departure from the U.S. and, if you fail to turn it in, you run the risk of being thought to have overstayed.