The phenomenon of combustion in Astrology signifies a planet getting too close to the Sun. Sun is a star and it has its own heat and light. Anything that gets close to the Sun would burn. Similar effects are felt by the planets when they get close to the Sun.
When the moon gets too close to the Sun we experience Amavasya which is due to combustion of Moon due to the Sun. Likewise, Mars, Mercury, Jupiter, Venus and Saturn, etc. all get combusted when they move very close to the Sun. Rahu and Ketu are free from the effects of combustion.
On 19th February 2013, Venus combusted in the east direction at around 12:29 pm. Currently Venus is transiting in Aquarius sign. Sun is transiting through Pisces at very close degrees to Venus, thereby causing combustion to Venus. It would get out of combustion on 21st April 2013 at around 04:05 pm.
A combusted planet has been defined as a "blind" planet and it fails to deliver its due results to the occupied house as well as the aspected house. All the significations and known results of the planet become weak.
Before understanding the effects of combusted Venus, we need to understand all the important aspects related to Venus. Venus is the key siginificator of marriage in Astrology. Whether a person would get married or not is analyzed by the position and strength of Venus in the horoscope. Likewise it is the planet that governs love, relationships, bonding in relationships and attraction among male/female gender. These are some factors that deliver happiness in everyone's life. When Venus will get combusted by the Sun, these aspects in life would get weak temporarily.
The learned people say that the following activities should not be undertaken when Venus is combusted.
Regarding marriage there are many popular beliefs. Normally it is said that either of the two Gurus (meaning planets here) i.e. Jupiter (Brihaspati) and Venus (Shukra) should not be combusted or in sign of debilitation (extreme weakness). Right now Jupiter is not combusted and neither in the sign of its debilitation. So marriages can be conducted during this period.
What should be done during this period?
It is advisable that prayers should be offered to the governing deity of Venus i.e Goddess Lakshmi. Direct prayers to Venus would also be helpful to ease the negative impact of combustion.
Those who are married should try to maintain harmony in their day to day life. The female spouse has been termed as the "Lakshmi" of the house. So she should be respected and kept happy especially during this period.
Best of Luck