The steps to get a passport will vary depending on the country you are coming from. However, the application process has a few general steps that are the same across almost all countries.
1. Get a passport application form - In the USA these are available from the Post Office and some government buildings. 
2. Get a passport sized photo. - The guidelines for this may vary between countries, but in the USA places like Walmart, Walgreens, and CVS are able to take these photos.
3. Fill out the application - You will need information such as your place of birth, any identification number you have such as a Social Security number, and information about your parents as well. 
4. Be prepared to turn in your birth certificate, drivers license, and possibly a second form of photo ID with the application.
5. Ensure that the application is complete. - Depending on the country you may be asked to turn in additional forms, staple your photos to the page, or leave certain sections blank.
6. Turn in the application in person to a passport office. - Some countries do interviews before accepting applications, some will require you to swear an oath, and some will require a filing fee.
7. Pay any fees to have your passport returned to you once it is printed. - This is in addition to any fees for application.
8. Wait for your passport to arrive.
This video walks you through the process of applying for a USA passport.
Reference 1: http://www.wikihow.com/Get-a-US-Passport
Reference 2: https://georgia.gov/blog/2013-10-03/getting-passport