What is the waiting time period between giving a depostion in a lawsuit and receiving a copy of the deposition?

It sounds to me like you have not retained an attorney to represent you in this matter since these are questions that your attorney would be able to answer for you. If you do not have an attorney then you will need to contact the court reporter and ask for your copy of the deposition and there could be a charge for your copy. At the time you gave your deposition you had the right to request that the court reporter furnish to you a copy of your deposition so that your could read it and and make any correction you might have to your answers to clarify or correct any error in your answer. The rule in Texas is that you have 30 days from the date that you receive your depostition to read it , make any corrections and then sign it and return it to the court reporter if you requested on the record to have the opportunity to read and sign your deposition prior to its filing.