It should take just a few weeks. You may check on the receipt of your appeal by using the Immigration Court Information System at 800 898-7180. Plug in your alien number and you will learn if your appeal has been received yet.
The answer to your question depends what type of decision you are appealing.
If you are appealing an Immigration Judge's decision to the Board of Immigration Appeals, the appeal is filed directly with the Board which usually issues a receipt within a few days after the appeal is received. In such a case you can expect to receive a receipt within a week or so. If you are appealing a USCIS decision to the Board the appeal is filed with USCIS and you can expect to receive a receipt for the appeal withing 2-3 weeks. If you are filing an appeal to the USCIS Administrative Appeals Office (AAO), the appeal is filed with USCIS and you can expect to receive a receipt in 2-3 weeks.
Appeals have very strict deadlines. It is important to make sure that you file the appeal with the correct office and the correct filing fee (or request for a fee waiver). Failure to do so can result in your appeal being dismissed as being untimely. You may want to consult with an immigration attorney who can ensure that your rights are protected during the appellate process.