In the name of Allah,

A Shia Muslim from Iran, student in Mechanical Engineering, Married, Interested in Religion, Philosophy, Math and Physics …

Islam means being "tasleem" (obeyer) in front of Allah, it starts with accepting this on tongue (without even having fully understood this, only due to some evolution in his hearth) and confessing that Allah is unique --a 1 with no 2 coming with or after him-- and that Muhammad S.A. is his created obeyer and his prophet, and continues until the person accepts no will for himself in front of the will of Allah.

Shia Islam is a branch of Islam, it started from the very first days after Muhammad-ol-Amin (muhammad the trustworthy) was chosen by Allah as Muhammad-Rasul-ol-lah (muhammad the prophet of Allah A.J.), when in a private ceremony the prophet introduced Ali A.S. as his succeeder, when Ali A.S. was only 9 or 10 and many people even had not accepted the prophet himself to be a prophet. Then Ali A.S. was reintroduced to the public as the prophet's succeeder in a place called Ghadeer-e-Khumm, and Shia Islam came to political scene after the prophet passed away …

The speech made in Ghadeer-e-Khumm by the prophet Muhammad S.A., more or less accepted by Shia and Sunni Muslims (see the book Al-Ghadir and also this book), is a great source for understanding Ideology of Islam and Shia Islam in particular, you can find it here (the speech itself starts from about the middle of the webpage) in English, also here in Arabic and here in Farsi.