The person is informed of the charges and a bail/release argument is made. Also both the prosecution and defense must serve certain notice pursuant to the Criminal procedure Law. Depending on the charges, there may be an offer of disposition.
It generally a fairly formulaic process. A plea of not guilty is entered, the DA may or may not request bail, and the case is then adjourned to a particular part, usually about 4 to 6 weeks later. During this time the defense attorney can invesitgate the case and begin discussions with the DA regarding any potential resolution.
It is always best to have an attorney at arraignment if possible.