Amber refers to two things: a set of molecular mechanical force fields for the simulation of biomolecules (which are in the public domain, and are used in a variety of simulation programs); and a package of molecular simulation programs which includes source code and demos.
Amber is distributed in two parts: AmberTools12 and Amber12. You can use AmberTools12 without Amber12, but not vice versa. See below for information on how to obtain Amber12.
A good general overview of the Amber codes can be found in: D.A. Case, T.E. Cheatham, III, T. Darden, H. Gohlke, R. Luo, K.M. Merz, Jr., A. Onufriev, C. Simmerling, B. Wang and R. Woods. The Amber biomolecular simulation programs. J. Computat. Chem. 26, 1668-1688 (2005).
An overview of the Amber protein force fields, and how they were developed, can be found in: J.W. Ponder and D.A. Case. Force fields for protein simulations. Adv. Prot. Chem. 66, 27-85 (2003). Similar information for nucleic acids is given by T.E. Cheatham, III and M.A. Young. Molecular dynamics simulation of nucleic acids: Successes, limitations and promise. Biopolymers 56, 232-256 (2001).
If you publish research that uses Amber you have to cite it as follows:
D.A. Case, T.A. Darden, T.E. Cheatham, III, C.L. Simmerling, J. Wang, R.E. Duke, R. Luo, R.C. Walker, W. Zhang, K.M. Merz, B. Roberts, S. Hayik, A. Roitberg, G. Seabra, J. Swails, A.W. Goetz, I. Kolossvai, K.F. Wong, F. Paesani, J. Vanicek, R.M. Wolf, J. Liu, X. Wu, S.R. Brozell, T. Steinbrecher, H. Gohlke, Q. Cai, X. Ye, J. Wang, M.-J. Hsieh, G. Cui, D.R. Roe, D.H. Mathews, M.G. Seetin, R. Salomon-Ferrer, C. Sagui, V. Babin, T. Luchko, S. Gusarov, A. Kovalenko, and P.A. Kollman (2012), AMBER 12, University of California, San Francisco.