The length of time if takes for an affirmative asylum application to be given a final approval or denial depends on many factors, such as how backed up the U.S. government is with applications, its current policy on handling backlogs, and the strength of your case (and therefore how many layers of decision maker it has to go through).
We'll discuss the typical progression and timeline here.
After you submit an application for asylum (I-589 and supporting documents) to U.S. Citizenship and Immigration Services (USCIS) by mail, the agency will need to review it for completeness, schedule you for a fingerprinting appointment, and later schedule you for an in-person interview at a local USCIS office.
At various times in the past, this has all taken place within a matter of months, at least for most applicants. More recently, however, USCIS has been so overwhelmed with applications that it has attempted to create various priority lists.
As of 2019, USCIS's priorities involved interviewing the most recent applicants FIRST, so as to deter people who were applying mainly to get a work permit (which one can, by law, only do if USCIS delays are long enough). That means many people who applied before the policy change will wait many months for an interview.
Of course, this policy could change again at any time. See USCIS's Affirmative Asylum Interview Scheduling page for the latest information on agency priorities.
The asylum interview itself is likely to take around 1/2 hour.
Once you have filed an asylum application, you can check the case status on the USCIS website.
After your interview, the Asylum Office should issue its decision within a matter of weeks. If you get an approval, that's great; you are an asylee, and on your way to qualifying for U.S. lawful permanent residence and eventually citizenship.
If you are not approved, and are not currently in valid status (for example, on a visa), you will be referred to another part of the U.S. government bureaucracy: the Immigration Court, or Executive Office of Immigration Review (EOIR).
The EOIR has its own issues with being overburdened with cases of people defending against removal (deportation). Unfortunately for one's chances of receiving a full hearing, the Trump Administration has tried to hurry cases along by instituting a quota system for deciding cases.
A "normal" EOIR hearing might take several hours. You, with the help of your attorney if you hire one (and you should), will testify and present evidence about your case so that the judge can consider the whole story. The attorney for the U.S. government Department of Homeland Security (DHS) will have a chance to cross-examine you.
If all this takes more than the allotted hours, the judge might order a "continuance," so that the hearing is resumed on another day.
At the end of the hearing or soon after, the judge will issue an oral or written decision. If the judge approves you for asylum, that's great; but it's not final until you find out whether the government plans to appeal to the Board of Immigration Appeals (B.I.A.).
If the DHS attorney "reserves appeal," then you'll have to wait approximately 30 days to find out whether the DHS attorney does, in fact, file an appeal (on Form EOIR-26), with a copy sent to you.
If the DHS attorney doesn't appeal, the judge's decision is final, and you are an asylee. Read more on what to do once you have received asylum.
If the DHS attorney does appeal, then another long wait lies ahead of you, while the B.I.A. considers your case. You won't need to appear in person, but should have an attorney file a legal brief on your behalf, explaining why the judge made a mistake and you deserve asylum after all.
The B.I.A. decision often takes around a year to receive. Once again, the decision could go in your favor, but the U.S. government could file an appeal, and you'd have to wait even longer for a final decision.
If either you or the DHS attorney appeals the B.I.A. decision, then the next step is to the federal circuit court of appeals, and after that the Supreme Court.
At this point, you are no longer within the immigration system, and thus it's impossible to say what you should expect in terms of timing. Federal court appeals do, however, commonly take months or years to complete. You'd seriously need a lawyer's help for this.