There are certain surahs in the Quran that Allah has given preference over others and have made them a means of healing, answering prayers, protection, etc. Below is one such example,
It has been narrated in Bukhari and Muslim from `A'isha (Allah be pleased with her) that, "When the Prophet (Allah bless him and give him peace) use to take his place of resting, he used to blow into his two hands and recite the Mu`awwadhat [Surah al-Ikhlas, al-Falaq, al-Naas] and pass and wipe his hands over the body.'
There is one thing to remember though. There is a difference between what is authentic prophet practice and what isn't. There are certain surahs you recite for a certain number of times and do the recommend act, like above. What some do is extend this by adding their own formulas where they state ridiculous stuff like recite this 7000 or that 300 times and do this or that to get what you want. That is not part of Islam.
Regarding the rain, there are also certain times that your dua (supplication) is more likely to accepted. A humanistic way of understanding is, you are more likely to get what you want if you go ask someone when they are in a good mood.
Narrated Sahel Ibn Sa'ad (RA): that the Messenger of Allah (SAW) said: 'Two will not be rejected, Supplication when the Adhan (call of prayer) is being called, and at the time of the rain'. [Al-Hakim 2: 114, and Abu Dawud #2540, ibn Majah]
'Seek the response to your du'as when the armies meet, and the prayer is called, and when rain falls' [reported by Imam al-Shafi' in al-Umm, al-Sahihah #1469]. The time of the rain is a time of mercy from Allah (SWT) so, one should take advantage of this time when Allah (SWT) is having mercy on His slaves.
You can read more about best time to make duas here http://www.islamawareness.net/Dua/best.html