"[Observing Saum (fasts)] for a fixed number of days, but if any of you is ill or on a journey, the same number (should be made up) from other days. And as for those who can fast with difficulty, (e.g. an old man, etc.), they have (a choice either to fast or) to feed a Miskin (poor person) (for every day). But whoever does good of his own accord, it is better for him. And that you fast, it is better for you if only you know.
The month of Ramadan in which was revealed the Qur'an, a guidance for mankind and clear proofs for the guidance and the criterion (between right and wrong). So whoever of you sights (the crescent on the first night of) the month (of Ramadan i.e. is present at his home), he must observe Saum (fasts) that month, and whoever is ill or on a journey, the same number [of days which one did not observe Saum (fasts) must be made up] from other days. Allah intends for you ease, and He does not want to make things difficult for you. (He wants that you) must complete the same number (of days), and that you must magnify Allah [i.e. to say Takbir (Allahu-Akbar; Allah is the Most Great) on seeing the crescent of the months of Ramadan and Shawwal] for having guided you so that you may be grateful to Him."
Narrated 'Abdullah bin Ma'qal
I sat with Ka'b bin 'Ujra and asked him about the Fidya. He replied, "This revelation was revealed concerning my case especially, but it is also for you in general. I was carried to Allah's Apostle and the lice were falling in great number on my face. The Prophet said, "I have never thought that your ailment (or struggle) has reached to such an extent as I see. Can you afford a sheep?" I replied in the negative. He then said, "Fast for three days, or feed six poor persons each with half a Sa of food." (1 Sa = 3 Kilograms approx.)
(Sahih Bukhari, Vol. 3, Book 28, No. 43)