After submitting a Form I-589 application for asylum to U.S. Citizenship and Immigration Services (USCIS), your next step is to await an interview at a local asylum office. (We're not talking here about cases where the person is in deportation/removal proceedings before the immigration court, but rather about voluntary, "affirmative" asylum submissions.)
How long that wait will be has varied over the years, from a few months to much, much longer. And the recent influx of migrants across the U.S.'s Southern border has made that wait extremely long of late.
You can find out how long you are likely to wait by going to a new chart that USCIS is providing. First, look in the left column for the office serving your region. Then count the number of months between the middle and right column to see how long the current wait for an interview is.
If you look, for example, at the chart posted in August of 2015, you will see that the San Francisco asylum office was, in July 2015, finally getting around to interviewing people who applied for asylum in July of 2013 -- a two-year wait.
It's not a pretty picture. As pointed out by Jason Dzubow in his column "The Asylumist," "cases are moving very slowly at most asylum offices, and a few offices–notably Chicago, Los Angeles, and Miami–have made no discernible progress in the last four months."
At least you can rest assured that your case hasn't been left behind as other people receive interviews faster than you. Your file probably hasn't been lost. (But if you don't get a receipt notice, that's a possibility worth checking into, as well.)