The City of Albany’s exams are all related to the requirements of specific job categories; they are not general tests of intelligence or ability. Therefore the first way to prepare for the exam is to get an exam announcement and read it carefully. The "scope" of the exam will provide a lot of information including the form of the exam (written, oral, evaluation of training and experience), the weight given to each part and the subjects to be tested.
Once you know the content of the exam, there are a couple of approaches to getting ready. One is to use a review or test book in the area to be tested. For example, if writing skills will be tested, a good grammar textbook may be the place to start. Another possibility is to look at the Civil Service review books (e.g., Arco series) in the public library for sample questions and answers. Even if there isn’t a review book for exactly the test you’re taking, there may be others that include the same topics. Compare the scopes of the two exams to find out. In addition, many of those books contain general strategies for test taking: how to stay calm, how to study, etc., and they can provide useful information to help in your preparation.
There may also be a study guide for your examination available on the New York State Civil Service website.