First ensure that the Zmanim jar (download) is in your classpath Import the package and create an instance of either the AstronomicalCalendar, ZmanimCalendar or ComplexZmanimCalendar. 
String locationName = "Lakewood, NJ";
double latitude = 40.096; //Lakewood, NJ
double longitude = -74.222; //Lakewood, NJ
double elevation = 0; //optional elevation
TimeZone timeZone = TimeZone.getTimeZone("America/New_York");
GeoLocation location = new GeoLocation(locationName, latitude, longitude, elevation, timeZone);
ComplexZmanimCalendar czc = new ComplexZmanimCalendar(location);
Note: The TimeZone has to be a valid timezone listed in the java.util.TimeZone.getAvailableIDs(). Note: For locations such as Israel where the beginning and end of dailight savings time can fluctuate from year to year, create a SimpleTimeZone with the known start and end of DST. To generate zmanim, invoke: 
Date sunrise = czc.getSunrise();
Date alos16 = czc.getAlos16point1Degrees();
The date that zmanim are generated for are stored in the Calendar object within the ZmanimCalendar. By default it is the date that the ZmanimCalendar was created. It can easily be reset in many ways. 
czc.getCalendar().set(1969, Calendar.FEBRUARY, 8);
or 
czc.setCalendar(new GregorianCalendar(1969, Calendar.FEBRUARY, 8));
when generating zmanim for a range of dates, the date can be rolled forward 
czc.getCalendar().roll(Calendar.DAY_OF_YEAR, 1);
The real power of this API is the ease in calculating zmanim that are not part of the API. The mothods for doing zmanim calculations not present in the ComplexZmanimCalendar or it’s superclass the ZmanimCalendar are contained in the AstronomicalCalendar, the base class of the calendars in our API since they are generic methods for calculating time based on degrees or time before or after sunrise and sunset and are of interest for calculation beyond zmanim calculations. Here are some examples: To get alos calculated as 14º below the horizon (as calculated in the calendars published in Montreal) add AstronomicalCalendar.ASTRONOMICAL_ZENITH (90º) to the 14º offset (measurements are from the vertical, so sunrise and sunset are 90º below the vertical): 
Date alos14 = czc.getSunriseOffsetByDegrees(AstronomicalCalendar.ASTRONOMICAL_ZENITH + 14);
To get the time of mincha gedola calculated based on the MGA using a shaah zmanis based on the day starting 16.1º below the horizon (and ending 16.1º after sunset) the following calculation can be used: 
Date minchaGedola = czc.getTimeOffset(czc.getAlos16point1Degrees(), czc.getShaahZmanis16Point1Degrees() * 6.5);
A slightly more complex example would be calculating plag hamincha based on a shaah zmanis that is not present in this API. While a drop more complex it is still rather easy. For example if you wanted to calculate plag based on the day starting 12º before sunrise and ending 12º after sunset as calculated in the calendars in Manchester, England (there is nothing that would prevent your calculating the day using sunrise and sunset offsets that are not identical degrees, but this would lead to chatzos being a time other than the solar transit (solar midday)). The steps involved would be to first calculate the shaah zmanis and than use that time in milliseconds to calculate 10.75 hours after sunrise starting at 12º before sunset 
long shaahZmanis = czc.getSolarHour(czc.getSunriseOffsetByDegrees(AstronomicalCalendar.ASTRONOMICAL_ZENITH + 12), czc.getSunriseOffsetByDegrees(AstronomicalCalendar.ASTRONOMICAL_ZENITH + 12));
Date plag = getTimeOffset(czc.getSunriseOffsetByDegrees(AstronomicalCalendar.ASTRONOMICAL_ZENITH + 12), shaahZmanis * 10.75);
Below is a full example (from the FAQ: Where is the Zmanim API Main Method?) of a very simple zmanim program that outputs sunrise, sof zman krias shema and sunset for the current day in Lakewood, NJ. Please ensure that the Zmanim jar (download) is in your classpath. 
/**
 * This program is a simple demonstration of the kosherjava.com Zmanim API.
 * To compile, ensure that the Zmanim Jar is in your classpath.
 */
import net.sourceforge.zmanim.*;
import net.sourceforge.zmanim.util.*;
import java.util.TimeZone;
public class SimpleZmanim{
	public static void main(String [] args) {
		String locationName = "Lakewood, NJ";
		double latitude = 40.096; //latitude of Lakewood, NJ
		double longitude = -74.222; //longitude of Lakewood, NJ
		double elevation = 0; //optional elevation
		//use a Valid Olson Database timezone listed in java.util.TimeZone.getAvailableIDs()
		TimeZone timeZone = TimeZone.getTimeZone("America/New_York");
		//create the location object
		GeoLocation location = new GeoLocation(locationName, latitude, longitude, elevation, timeZone);
		//create the ZmanimCalendar
		ZmanimCalendar zc = new ZmanimCalendar(location);
		//optionally set the internal calendar
		//zc.getCalendar().set(1969, Calendar.FEBRUARY, 8);
		System.out.println("Today's Zmanim for " + locationName);
		System.out.println("Sunrise: " + zc.getSunrise()); //output sunrise
		System.out.println("Sof Zman Shema GRA: " + zc.getSofZmanShmaGRA()); //output Sof Zman Shema GRA
		System.out.println("Sunset: " + zc.getSunset()); //output sunset
	}
}
The following would compile and execute this code (sample from a DOS prompt in Windows). 
C:\path\to\code>javac SimpleZmanim.java

C:\path\to\code>java SimpleZmanim

Today's Zmanim for Lakewood, NJ
Sunrise: Thu Nov 05 06:30:27 EST 2009
Sof Zman Shema GRA: Thu Nov 05 09:05:21 EST 2009
Sunset: Thu Nov 05 16:50:02 EST 2009
Please see the Zmanim API documentation for a more complete view of the API.

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