The exact procedure of getting the user credentials depends on the organisation involved.
As an example the procedure for getting the credentials in CERN can be found from:
http://globus.home.cern.ch/globus/ca/#usercert
Again the Globus grid-cert-request is used, but without arguments.
grid-cert-request
Then the certificate request file .globus/usercert_request.pem is send to the CA involved. After the CA has signed it and returns the certificate, the returned certificate has to be saved to the .globus directory with name usercert.pem.
After this is done the credentials are ready and the grid-proxy can be created using the globus command grid-proxy-init or, when using VOMS, using voms-proxy-init.