In addition, it will list the items that you need to bring with you when returning the form to apply for your CHL. The basic list is:
Some sheriffs ask for additional information on their forms. The most common addition is asking you to provide some number of "character references". In many (most?) cases, these are never actually used, but just in case they are it is wise to let the people whose names you use know, and even more importantly, know how they will respond! Think of this as giving references for a job. You would not list someone that you knew, or suspected might give you a bad reference.
For non-US citizens, you will need to produce evidence of your right to residence in the USA (e.g. green card), and some evidence of your intent to obtain US citizenship. There is an immigration form (N300) specifically for this purpose. This form was originally the first stage in the citizenship application process, but is no longer required for that purpose. It continues to exist because some states have legislation requiring it. Unfortunately, the Federal government sees this form as an excuse to make money, and although the process to obtain one is easy (apart from sitting in an immigration office for many hours waiting your turn) the cost is exorbitant ($235). If you are a non-citizen, contact your local sheriff's office and ask what paperwork they require. If you have started the citizenship process, a copy of your application should be sufficient. If you have to get a "Declaration of intent to become a US citizen", it is a form which is meaningless to the Federal government, does not begin the citizen application process, and does not commit you to becoming a US citizen. If you are not a US citizen, the law requires that you be resident in the county where you make your application for at least 6 months. You need some way to document this. Suitable documentation might be rent receipts, electricity bills etc. These would need to be in your name of course.
Once you have completed your form and assembled all the required paperwork, the next step is a visit to your local sheriff's office to make the application.
How this works depends upon your local sheriff. In some cases there are dedicated staff who will receive and process your application at any time during normal working hours. In other cases specific times and days are set aside to process CHL applications. In other cases, you will have to mail in the completed form and wait for an appointment to go into the office. Check the process and times when you pick up your application form.
Do not take your gun with you when you go to the sheriff's office.
When you make the application, you will be photographed and your fingerprints taken. Depending upon how well financed your county sheriff's office is, they may be equipped with the latest "no-ink" fingerprinting systems. In other cases you will get inky fingers (but they always provide you with the materials to clean up, and the ink comes off easily when the right cleaning materials are used).
Once the application process is complete, they will send you away with a warning that it can take up to 45 days to process the background check, and that until you receive the CHL you may not carry a concealed firearm. In many cases, processing is complete in much less time.
This requires a trip to the sheriff's office. If they decide that the photo that they have is out of date they will take another photo. They will take your old CHL and give you a receipt which acts as a temporary replacement for your CHL (I would not rely upon the receipt in states that recognize an Oregon CHL). The replacement arrives in the mail a few days to weeks later.