The application can be completed online at
FCC Universal Licensing System (ULS): ULS Home with the FCC Universal Licensing System.
Here's an excerpt from the AOPA...
Originally Posted by www.aopa.org
Members must receive an FCC registration number (FRN) before completing the application for the FCC Restricted Radio Telephone Operator Permits or FCC Radio Station Licenses. FCC Form 160 must be completed to obtain an FRN. FCC Form 605 and FCC Form 159 must be completed using the FRN to obtain the permit and licenses.
AOPA encourages members to use the FCC's Universal Licensing System to complete and submit all FCC applications (159, 160, 605). This systems returns the FRN immediately allowing completion of the 605 and 159 forms. Users are prompted for required information, thus alleviating the submission of incomplete forms. Applicants using paper forms may face delays from the Postal Service and incomplete forms causing forfeiture of the application fee.