A visa does not guarantee entry. At the US airport, a CBP officer (Customs and Border Protection, the border police) checks the papers and decides if your parents may enter and for how long. Good papers make this short and calm.
If you are the adult child here, make this list with your parents a week before the flight.
Papers to carry in the hand bag
Passport, valid for the whole trip, with the B-2 visa inside. Parents from Visa Waiver countries need an approved ESTA instead.
Return ticket or the booking printout. For ESTA travelers a round-trip or onward ticket is required. For B-2 visitors it is strong proof they plan to go home.
Invitation letter from you: your name, status, address, phone number, the visit dates and the reason (for example, "to visit me and meet our new baby"). It is not required, but it helps.
Your US address written on paper and saved on their phone. The officer and the customs form ask for it.
Proof of funds: a recent bank statement, or a letter from you saying you will pay costs, with your own bank statement.
Visitor insurance card and the insurer's phone number.
Proof of ties at home, if they have it: pension letter, property paper, a letter about a job or family duties.
Keep medicines in the original pharmacy box or bottle with the label.
Carry a copy of the prescription or a doctor's letter, in English if possible.
Bring only a personal amount for the trip. Some medicines sold abroad are not allowed in the US.
Declare all medicine and food on arrival. See Customs: food, cash, medicines and gifts.
Questions are short. Practice simple, true answers:
"Why are you visiting?" — "To visit my son and his family."
"How long will you stay?" — Give a clear plan, such as "Three months, until March 15."
"Where will you stay?" — Your address.
"Who pays for the trip?" — "I do" or "My daughter does."
"What do you do at home?" — "I am retired."
It is fine to say "Please repeat" or "I do not understand." Never guess or say what they think the officer wants to hear. Do not say they are coming to work, babysit for money or move here.
Carry-on (hand bag): passport, all papers above, medicines for at least a few days, glasses, a phone with a charger, and a pen for forms.
Checked bag: clothes, gifts, extra medicine supplies, and packed food (declare it).
Carrying more than $10,000 in cash or similar, all travelers together, must be declared.
Within a few days, check their I-94 at i94.cbp.dhs.gov. The date there is the last day they may stay, not the visa date.
Packing the passport or prescriptions in the checked bag.
An invitation letter that promises a very long stay.
No phone number for you written on paper in case the phone dies.