what process is needed to invite foreigner for visit

There is no process. The foreigner simply applies for a visitor visa by completing a DS-160 and scheduling an interview at the U.S. Embassy. You are free to provide a letter of invitation for the foreigner to take to his/her visa interview, but these documents are given little weight. The foreigner will need to credibly establish the reason for his/her trip as well as ties to his/her country that make it likely he/she will return.