There is always confusion of moon sighting and deciding on Eid but I hear somewhere that the moon need to be a certain percentage to say it will be Eid next day. If that is true then what is a percentage of the moon sighting?
First, there's no confusion of moon sighting at all either the new moon (or the crescent moon) can be seen or not. This may need to some extent trained people a good location for a clear sighting and the sighting to be made during a fixed time gap and the sky to be clear. The later is somewhat difficult in for example big cities etc. but easier to realize somewhere out in a desert or in the countryside. And you may see something like in this link.
The confusion comes from different positions of scholars: Some say a global sighting is binding for all Muslims. Others say only a local sighting is. I've posted the discussion and evidence of both sides in my answer on "What are the opinions on moonsighting as per the classical scholars?".
A percentage appears in calculations of the possibility of a moon sighting. Note that the new moon needs a certain time gap to be possibly seen by naked eyes. A simple explanation: Assuming the new moon was born yesterday at 9 p.m. it might —for example— only be seen from today 9 a.m. or later and the calculation or prediction of a possible moon sighting can be based on certain percentage. This is due to the fact that the moon needs some 27.3 days to circle around the earth while a full moon cycle is of 29,53 days so the moon "disappears" as it can't reflect the sunlight for a certain time.
See also on moonsighting.com under the faq's a more correct explanation:
2.1 Question: After the Moon Birth, how much time is required for people to sight the New Moon?
Answer: Time passed after New Moon Birth is called the age of the moon. Sighting is possible at different age in different months. So, age cannot be a criterion for sighting. Why is it so? Because, the orbit of the moon is elliptical and in its orbit, the moon moves faster when it is closer to the earth, and slower when it is farther from earth. When it moves faster, the moon becomes visible at smaller age (like 17 hours), and when it moves slower, it becomes visible at larger age (like 23 hours). The main factor that makes the moon visible is the angle between moon-earth-sun. When this angle becomes about 9 degrees, the moon starts to be visible. How much time it takes to get this angle depends upon the speed of the moon in its orbit.
The ECFR (European Council for Fatwa and Research) and ISNA (The Islamic Society of North America) —sadly— adopted the calculation method used by the the Turkish Diyanet which uses the criterion of "altitude > 5°, elongation > 8° anywhere" in their calculation, which is used to predict a global sighting, but has some flaws when the calculated prediction moves over at the international date line. Note that AMJA (The Assembly of Muslim Jurists of America) still adopts a moonsighting methodology, which is the most-followed authority among Sunni Muslims in North America.
If we consider the lunar phases strictly speaking new moon or the phase where the moon can't be seen is not the beginning of the Islamic month, but the first possible crescent so once a small crescent is possible to be seen at the fixed time gap the new Islamic month would begin this would apply to May 9th in this Wikipedia May-June Calendar 2005.