If you're filing an N-600 form (Application for Certification of Citizenship, issued by U.S. Citizenship and Immigration Services or USCIS), then it means you believe you have acquired or derived U.S. citizenship based on your parents status as American-born or naturalized U.S. citizens. In essence, the form says to the U.S. government, "I am a U.S. citizen by operation of law, please give me a certificate to prove it."
So if you've correctly analyzed the law, and your right to U.S. citizenship, you don't have to wait for approval to call yourself a U.S. citizen -- you are already a U.S. citizen.
The processing time for the N-600 application form depends on how backed up your local USCIS office is. You can check this by going to the page of the USCIS website's "USCIS Processing Time Information" page and choosing your local field office from the drop-down menu. Depending on how smoothly the process goes, you can expect to wait a few months before your application is approved. Obviously, some applications are denied, making the time frame much longer.
The law in this area is extremely complicated, and depends on the year in which you were born. For example, if you were born between November 14, 1986 and the present, and both your parents were U.S. citizens, and at least one of them had a prior residence in the U.S., then you automatically acquired U.S. citizenship. But if only one of your parent was a U.S. citizen when you were born, that parent must have lived in the U.S. for at least five years and at least two of those years must have been after your parent reached the age of 14.
But the laws changed many times over the years, so if you were born before November 14, 1986, you'll need to figure out which laws apply and whether they allow you to claim U.S. citizenship based on acquisition.
Here again, whether you have derived U.S. citizenship depends on whether and when certain important events occurred.
For example, if one of your parents was born in the U.S. or naturalized between February 27, 2001 and the present, and you have a green card, and the naturalization if any took place prior to your 18th birthday and while you were living in the U.S. in the legal and physical custody of that parent, then you have derived U.S. citizenship. Once again, however, you'll need to check the various laws over the years to find out what applies to you.
If you have acquired or derived U.S. citizenship, another possibility open to you is to apply for a U.S. passport as proof of your status. You don't need to wait until you get a certificate of citizenship -- though it might be easier if you do wait.
An experienced immigration attorney can help you analyze the laws that apply to your case and prepare a successful application for a Certification of Citizenship. For a summary of these laws over the years, see U.S. Immigration Made Easy, by Ilona Bray (Nolo).