2 days ago my political asylum case was denied by the immigration judge.How long the appeal process usually takes?

When the BIA responds to your filing of the EOIR-26, it will include a copy of the transcript of your removal hearing(s). Carefully review the transcript and any documentation filed with the immigration judge before preparing an appellate brief and do any legal research needed to back up your case. Be sure to note which cases from the U.S. Circuit Court having jurisdiction over your area are relevant or persuasive to your case. Be aware that an appeal is based on questions of law (and whether or not it was correctly applied) and not questions of re-arguing facts. You will need to send copies of anything you file with the BIA to the government's attorney as well. Depending on how thoroughly you prepare your appeal (you'll need to be sure to follow EOIR--Executive Office of Immigration Review, court procedures for filing and brief format as well), you may expect an answer in either a relatively short time (generally indicating that you've lost on appeal) or a matter of weeks or months before receiving a decision (my experience has been the longer, the better) as to whether you have "won" on appeal regarding the matter and/or whether your case will be remanded (sent back) to the immigrant judge to make a new decision based on the findings of the BIA. Everything is done on paper. Always use proof of mailing and keep copies of everything. BIA decisions are sent in the mail. All that being said, I think it worth your time and financial investment to consult with an immigration attorney experienced in filing appeals with the BIA both to see what your chances on winning on appeal are, and if fair, then to handle researching and writing the appeal on your behalf. Best of luck!