When you arrive back in the U.S., you will be asked whether you purchased goods worth more than $800 while abroad. In some airports, the question is asked at a little electronic kiosk where you have to indicate "YES" or "NO" to that question and a couple of other questions. In other airports, it might be a hand written form that you fill out. (I think all airports are eventually going to the kiosks so that your answers are recorded.) After answering those questions, a receipt is issued by the kiosk that you take with you to Passport Control and then on to the luggage carousels. After picking up your luggage, you take that receipt, your luggage and your passport to the Customs agent who is the last stop before you are released back into the country. They take a look at the receipt and your passport one more time. Sometimes, even when you answered "yes" to the question of whether you purchased $800 or more abroad, they just waive you through. Other times, the agents will ask more detailed questions and will send you to another agent who will examine your receipts and calculate how much you owe and process your payment. Sometimes, they pull people out of line who answered "no" to the question and search every bit of their luggage. (I've seen it happen.)
Generally, the first $800 is tax free. The next $1,000 is taxed at 3%. For handbags, amounts over $1,800 are taxed at 6%. (Other goods have different tax rates so it can get complicated. By the way, there is no tax on food items.) This limit applies per person
and you can combine these amounts for all the people in your traveling party. So, if you are traveling with your DH or SO or your mother or whoever, you can combine these amounts. So, for two people, the first $1,600 is tax free, the next $2,000 is taxed at 3%, and everything over $3,600 would be at 6%.
My experience has been that if you are honest, they treat you extremely well. When I have purchased more than $800 worth of stuff, I have always declared it and they have never searched my luggage. They take your word for what you have purchased abroad and calculate the duty based on that. A couple of times, they've waved me through and I paid nothing even though I did exceed the limits. The last time (just about a week ago) was hilarious. I was fully prepared to pay several hundred dollars in customs tax/duties when returning to the U.S. I did a lot of shopping for Christmas, for friends, for myself while in London. I declared at the kiosk that I had purchased more than $800 worth of items. At the last stop, the Customs Agent asked me "what did I purchase?". Well. I told him that I bought biscuits and tea and chocolate and re-usable bags from Fortnum & Masons and Harry Potter souvenirs for my neices and nephews and, oh, there was a . . . and he interrupts me and says "Welcome Home!" He never let me get to the Louis Vuitton and Chanel handbags in their original boxes. I stood there for a second and the DH grabs my arm and says "thanks, great to be home!" So, no customs tax charged.