First, during your flight to the United States, you'll be given a US Customs declaration form. Bring a pen in your carry-on. You can see a copy of the form online, along with instructions, so you know what to expect. If you have a specific question about the form, you can ask that here as a new question or ask one of the officers when you arrive in the US. It's far better to ask about something than to make a false declaration.
When your flight arrives at a US airport, you'll walk off the plane and be directed into a secure hallway. All passengers must go through US immigration and customs, even if you are only transiting the US. Follow the signs and the crowd to the Federal Inspection Services area (there's only one way to go). When you get there, you'll:
Follow signs to the appropriate line. Depending on the airport and terminal, the exact process may be slightly different, but there will be lines for US Citizens and various categories of visitors. There is usually staff in this area if you are unsure where to go.
Wait. The CBP website provides historical wait time information that may be of use in estimating how long this will take.
Immigration / passport control. Some visitors may use an automated kiosk first (the exact definitions about who uses the kiosks are a bit different at each airport, so simply follow the signs and you'll end up in the right place); simply follow the instructions to scan your passport and complete your declaration on the kiosk. Eventually, you'll end up at a booth with a US immigration officer. Present your passport and customs declaration form and answer any questions the officer may have about your trip (purpose of your trip, where are you staying, etc...). More about those questions below. Your fingerprints and photograph will be collected at this time. Assuming you are admitted, the officer will stamp your passport and direct you to the next step.
About that stamp: the officer will stamp your passport with an admission stamp. That stamp will indicate how long you may remain in the United States (generally up to six months for a B-1/B-2 visa holder), and it's important not to overstay. In some cases, the admission period may say "D/S," short for "duration of status." This means you may stay in the United States as long as you are "in status," such as while you are a full-time student for a student visa holder. If you're unsure when you must leave the country, you should ask.
Baggage claim. Check the TV monitors to see what carousel is serving your flight, go there, and pick up any checked luggage. You must pick up your checked luggage here when entering the US, even if you are connecting to another flight. There may be officers with trained dogs inspecting luggage in this area. Grab your bags, if you have any, and take them through:
Customs. Here, you'll present your declaration form to an officer, who may ask you a few questions about your possessions. At this point, you'll either be directed to the exit (which is typical) or selected for further scrutiny (which is not atypical, but less common). If selected, they may X-ray your bags and/or open them and look inside. They have the authority to search your bags and/or person. If you have any food or other items that you declared on your form, you'll be asked about them here or directed to a specialist.
Exit. Once you are done, you'll reach the exit. Here, there will be signs for "ground transportation" (if you plan to leave the airport) and "connecting flights" (if you will be boarding another flight). For connecting flights, there is a "bag drop" counter where you return your checked luggage to the airline so it will be checked onto your next flight. At this counter, you can ask the staff to ensure you know where to go for your connection. If you have a connection, you will go through TSA airport security before being allowed back into the terminal.
As a visa-holder, you have been "pre-vetted" by the Department of State, but admission to the United States is not guaranteed (compared to the number of travelers, the number of refusals, however, is very small). You will still be inspected by a Customs and Border Protection (CBP) officer. This may be as simple as a brief "hello," but may be a more involved process if their suspicions are raised. These are the types of questions you might be asked:
The purpose of your visit to the United States
How long you plan to visit
Where you will be staying
If you have the means to support yourself financially in the United States
If the documents you present match the purpose and intent of your visit
It is important to tell the truth. Sometimes visitors will try to hide something that really isn't a problem, but if you're caught lying, that will make the situation far worse. If you do not understand something, ask to clarify or request a translator.
There are no documents you must bring (besides, of course, your passport), but it may be helpful to carry some of the documents you brought to your visa interview in case you are asked for proof of funds. There is no minimum amount of money you must have, but you may be asked to show that you have sufficient funds to pay for your trip. This need not be in cash (and for safety reasons, probably shouldn't be): credit and debit cards are fine. If you are carrying more than $10,000 USD in currency, you'll have to declare that on your customs form and may be subject to more scrutiny.
You should also have the appropriate documents for the purpose of your trip. If you're visiting someone, you should know who that person is, their address, how to contact them, etc... If you're on vacation, you should know where you want to go, how you will get there, etc... They will be suspicious of someone who shows up at the border without really knowing why he is there or where he is going. It's fine to change your plans and be spontaneous later, but you should at least have a solid initial plan for where you're going.
Finally, US Customs and Border Protection has a website for international visitors with more information, including two videos about entering the United States that may be of use to first-time visitors.
