Obtain an application form by contacting the IPS if you live in the U.K. you can contact the office through its website (see Resources below). If you live outside the U.K. you'll need to go through Foreign and Commonwealth Office (see Resources below). You will be given the option of filling out the form online and having them send it to you for your signature and a qualified countersignature or they will send you the blank forms.
Fill out the form. When filling out the form whether online or paper versions be sure to use black ink and all capital letters, also leave squares that you don't fill in blank. Filling them in or putting slash marks through them could slow down your application's processing.
Sign the form and get someone to countersign it. The counter signatory must be someone who you have known for at least two years. They must be a member of a recognizable profession or has good standing in the community and willing to write their own passport number on your application. They will also need to verify, sign and date the back of one of your passport photos; seal up the packet, including document fees and birth certificate or naturalization papers, and send it off to the IPS.
Wait a couple of weeks, someone from an IPS office will contact you for an interview. Once you successfully verify your identity through this interview process the IPS will issue you a brand new passport.