If you mean an appeal from an immigration judge's denial of asylum then that is an appeal to the Board of Immigration Appeals. Those could take several months, even years, but there is no way to give you an accurate or precise estimate. It also depends on whether the person is detained or not, whether the appeal is dismissed summarily, etc.
If you mean an appeal from the Immigration Service's decision on an affirmative application that is actually not an appeal but a referral to the IJ. The IJ would then re-evaluate your case anew.
The issue is very very complicated and technical and so you would need an excellent appellate immigration attorney with a lot of experience. if you have completed the EOIR 26 it probably means you did it yourself so now seek excellent counsel, do NOT try to do by yourself as it is very very important to get good representation before the Board.