Unless you are familiar with PeopleSoft, I would think your client should guide you in this integration. PeopleSoft has various ways to communicate with the "outside" world and I can give you the link to the PeopleTools PeopleBooks (http://docs.oracle.com/cd/E17566_01/epm91pbr0/eng/psbooks/psft_homepage.htm) but I highly doubt that will help you when you don't have any experience with PeopleSoft.
Easiest option with sending to an outside application and receiving results is, in my opinion, still a webservice. But then your client should do some work as well otherwise they will never be able to send anything at all. Direct link to documentation on PeopleTools 8.52 would be http://docs.oracle.com/cd/E41509_01/pt852pbh2/eng/psbooks/tibr/book.htm