To cast a birth chart, i.e. the horoscope, the software application takes the four inputs - date of birth, time of birth, time zone and coordinates of the place of birth. Based on that, the application converts all the parameters to the local time of the place by first converting time based on time zone to UTC and then to the local time based on the longitude of the place. Once this is done, the calculations done to compute the position of planets, ascendant sign and sun rise, moon rise are pretty straightforward and can be found in any good astronomy text book.
The calculations are done for planets from Sun to Saturn along with Lunar Nodes - Rahu and Ketu. We give outer planets a skip - there are no Uranus, Neptune and Pluto in a Vedic horoscope. This is because these outer planets were discovered fairly recently and sages in ancient India did not know about them. Western astrologers were quick to adapt these planets in their readings, but rarely would you find any jyotishi refering to them. More so, these planets do not have any sign ownerships, nor do they appear in vimshottari dasha calculations.
Western astrology stops at this step of calculation. The display is called tropical position of planets that assumes the Zero of degree calculation is first point of Aries, i.e. position on 21st of March. For followers of Western Astrology, this may seem a bit odd, because planets change signs between the two systems. If you are a Libran according to the western system, you may find Sun situated in Virgo in a Vedic Astrology birth chart.
Ancient Indian astronomers discovered long back that these two points i.e. the Zero degree of measurement and the first point of Aries do not always coincide because our Earth is wobbling on its axis. They applied a correction to the degree calculated in the last step and called this Ayanamasha correction. It is difficult to make out the exact value of Ayanamsha correction just from observation of signs in the sky. For this, the great sages devised an ingenious method. They observed life of people around them, cast their birth charts and adjusted the degree of Ayanamsha correction.
In this site, I have used Lahiri's Chitrapaksha Ayanamsha, the value of which is 23° in 1938 and increases by 50.5 secs per year after that. We can find shlokas in various places that support this Ayanamsha and this ayanamsha alone has withstood the test of times.
Article @ www.planetarypositions.com