There is no simple answer. The discovery duration depends on complexity of a case, responsiveness of the parties in a lawsuit ( production of documents, expert reports, etc.) motions, and other factors. For example in new jersey state civil actions, as a general guidance, you may refer to rule 4:24 (http://www.judiciary.state.nj.us/rules/r4-24.htm) for time for completion of discovery. A court assigns a specific track to each pending action based on the complexity.
Disclaimer: This answer should not be relied upon as legal advice. I am admitted in the States of New Jersey and New York and before the United States Patent and Trademark Office only. The response above does not form an attorney-client relationship, nor it is intended to be anything other than the educated opinion of the author. Consult an attorney in your geographic area before you act on any of this advice.
As with most litigaton question, there's no 1-size-fits-all answer. There are lots of independent discovery methods, and every case is different, so this is something you need to go over with your own lawyer about your own case.
Sometimes parties and witnesses can be deposed in a week from giving them notice. Sometimes parties and witnesses respond to written requests for documents and answers and admissions in a month.
Sometimes they fail or refuse to respond, or respond incompletely, and the requesting lawyer has to file a motion to get the court to compel their compliane. Sometimes parties block subpoenaed witnesses from cooperatin by moving to quash the subpoenas. Discovery battles can go on literally for years, since that's often where cases are won or lost, based on that evidence.
Disclaimer: I'm only licensed in CA. Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.