Is the application for GC going to be processed as an adjustment of status (applying in the US) or via a immigrant visa (applying from overseas)?
If in the US then it depends on how long it takes your current local office to process I-485 applications. When my wife adjusted her status it took 83 days for her to get her GC (Baltimore, MD applied Dec 2009, received Mar 2010).
If outside of the US then the entire process can take about a year. My wife submitted the I-130 petition for Alien Relative in June 2013 and it is still pending. Once approved then it needs to be processed by the State Department and her parents will have an interview at the local embassy overseas. When the visa is approved and they arrive in the US then they will become automatic GC holders.
However, each case is different and the processing times are always changing.