Assassin
It comes from the French/Italian word Assassini, which comes from the Arabic word Hashshashin.
It referred to a group of Nazari Isma'eeli Shi'a Mohammedan Muslims who were called The Order of the Assassins.
Only a set of disciples called the Fedayeen actually involved in fights.
Origin of the Word
"Asas" means "principles" in Arabic. "Asaasiyyoon" meant "People of Principles". "Hashshashin" was probably a play on the word "Assaasiyyoon" (not "Assaassiyyeen", the plural of "Asasi", meaning Fundamentalists).
"Hashshashin" means "hashish users". Hashish is a tobacco based drug.
The term Assassin was introduced to Europe by Marco Polo.
Alternate Explanation
According to Lebanese writer Amin Maalouf, the real etymology is from when Hassan-i Sabbah used to call his disciples Asaaseeyoon (meaning Fundamentalists). He based this on the texts from Alamut.
History of the Hashish Term
The term Hashishi was first used back in 1122 during the fall of the Fatimid Khilafat, by Mustali Isma'eeli Kalifa al-Amir bi-Ahkami'llah to pejoratively describe his enemies, the Assassin Isma'eelis of Syria. He was assassinated.
This term was then used by many anti-Isma'eeli historians to describe the Isma'eelis of Syria and Persia.
To the Crusaders, the Fedayeen concept of valuing a principle above your own life was alien, so they rationalized it using myths such as the 'paradise legend', 'leap of faith' and the 'hashish legend'. This was found in Marco Polo's works.
19th century orientalist Silvestre de Sacy was the first to link the etymology of Assassin to Hashih using the variants "assassin" and "assassini". He used 13th century historial Abu Shama's record to do so.
Self-proclaimed Sufi scholar Idriesh Shah (who didn't belong to any Sufi Tariqa or graduated from any university) then continued to pejoratively affirm that the Assassins, and Isma'eelis in general were druggers who used hashih to stupefy candidates for sending them to paradise.