Volunteering in Islam: During the Prophet, sallallaahu 'alayhi wa sallam, time and our guided Caliphs was there any type of volunteering without getting any financial remuneration? Or were volunteers paid for their volunteer work? Also, can you elaborate more about the concept of volunteering in Islam and how does it fit in our daily lives?
May Allah reward us and guide all Muslims to the straight path.

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

There is no religion or nation or law that gave volunteering acts as much importance as Islam did. The pieces of evidence proving this fact are uncountable in the sources of Islamic Sharee’ah. We mention here a few of them from the Quran, the Sunnah and sayings of the righteous predecessors.

Evidence from the Quran: Allah Says (what means):

{… But whatever thing you spend [in His cause] - He will compensate it; and He is the best of providers."} [Quran 34:39]
{No good is there in much of their private conversation, except for those who enjoin charity or that which is right or conciliation between people. And whoever does that seeking means to the approval of Allah - then We are going to give him a great reward.} [ Quran 4:114]
{But he has not broken through the difficult pass. And what can make you know what is [breaking through] the difficult pass? It is the freeing of a slave. Or feeding on a day of severe hunger. An orphan of near relationship. Or a needy person in misery.} [ Quran 90:11-16]
{Have you seen the one who denies the Recompense? For that is the one who drives away the orphan. And does not encourage the feeding of the poor.} [Quran 107:1-3]
{And they feed, for the love of Allah, the indigent, the orphan, and the captive.} [Quran 76:8]
{And cooperate in righteousness and piety, but do not cooperate in sin and aggression.} [Quran 5:2].
{… and do good - that you may succeed.} [Quran 22:77]

Evidence from the Sunnah:

The Prophet said:

“The dearest to Allah is the one who is most beneficial to people. The dearest deed to Allah is bringing happiness to a Muslim, or dispelling a grief from him, or settling his debt, or feeding him while he is hungry. It is dearer to me to support my Muslim brother to satisfy need than to make one month I'tikaf in the mosque. Whoever controls his anger Allah will cover his faults. And whoever goes out with a Muslim till he fulfills his necessity, Allah will make his feet stable on the Day while feet slip. [At-Tabarani , Sheykh al-Albaani graded it as Hassan in Saheeh al-Jami’] A Muslim is a brother of another Muslim, so he should not oppress him, nor should he hand him over to an oppressor. Whoever fulfills the needs of his brother, Allah will fulfill his needs; whoever brings his (Muslim) brother out of discomfort, Allah will bring him out of the discomforts of the Day of Resurrection, and whoever screens a Muslim, Allah will screen him on the Day of Resurrection.”
“One who guides to something good has a reward similar to that of its doer.”  [ Muslim ]

As for your question, about whether or not there was volunteering in the period of Prophet and the rightly guided Caliphs, then the answer is that most of the deeds were carried out voluntarily; you may find details in the books of Islamic history and biography.

The aspect of volunteering in Islam has deep roots and needs a lot of time and separate books to be explained.

As for implementing this act in present day, there are lots of charity, social and relief organizations everywhere in the world, though they are facing a hard time from the enemies of Islam.

Finally, we urge Muslims to intensify their voluntary acts individually and in groups. We ask Allah to ease the matters of the Muslims.

Allah knows best.