First of all, it should be checked how the boy got divorced in the US, whether it was by mutual consent or otherwise. The divorce order needs to be studied as to its conditions, if any. It has to be ensured that the boy has not married again. If the marriage is to take place now in India according to Hindu custom, it can be so performed and registered in accordance with the Hindu Marriage Act. Please comply with the procedure laid down by the jurisdictional Marriage Officer for registering the marriage by producing the documents required which are generally ID and address proofs, divorce decrees, marriage invitation, photograph of the couple, and the presence of  two witnesseses.

They can get married in India through special marriage Act

What is ground for divorce in USA 

no fault divorce obtained in USA is not valid in India 

your do or r decree will not be valid in India 

get divorced in india  then re marry 

The marriage requires registration either under Special Marriage Act or Hindu Marriage Act.

The prove of divorce , identity proof and residence proof are general documents required for registration. Else the Marriage Registrar would guide you properly. 

They both can get married under the provisions of special marriage act.

They have to comply with all the requirements including marital status certificate from his embassy or authorities of his country and comply with other procedures as prescribed in the provisions of law for solemnising marriage under special marriage act.

basic Id cards, matriculation marksheets, address proofs, contact below for rest 

Since you said both boy and girl are Hindus.

Since you said boy is US citizen who got married in India and divorced at US

Since you said that both wanted to get married in India 

Unless the divorce of boy is held valid in India, second marriage cannot be performed.

So please give details as to how and on what ground boy obtained divorce in US and whether such divorce obtained in US is valid as per Indian laws.

If boy's divorce is valid, then safest procedure for the second marriage is to get married under the provisions of special marriage act (normally we call it as register marriage).

They need to possess their earlier divorce decree and their respective Identity as well as address proof and witnesses.