If customers are asking for GFSI Certification they don't know what they are asking. There is no such thing for food companies.
GFSI are an organization that have created Food Safety Management System documents, so that Standards owners such as BRC, IFS, SQF and FSSC can apply for their own standards to be compared to the GFSI blueprint and if they are found to be adequate then they become GFSI approved.
That's pretty much all you need to know about GFSI.
As a food business your interest is with the Certification Body e.g. BRC, IFS, SQF and FSSC (there are others but they are the main ones). They all have their own GFSI approved standards which are similar, but have the same goal, which is to provide requirements for an effective food safety system.
First you need to decide which standard (BRC, IFS, SQF and FSSC) you prefer and usually this is done by surveying the opinions of customers to see if they have a preference.
Once chosen you work to develop your system to meet the requirements (and you will get a lot of help here doing that). Then when you are ready you contract a Certification Body to conduct an audit of your business. Hopefully they will find only a few minor nonconformities which you need to correct before getting your certificate.
Regards,
Simon