The term ‘Ijtihad’ derived from ‘jahd’ [1]literally means "to endeavor, strive, put oneself out, work hard. Also, it means ability and competence, if the root word is ‘johd’[2]. In Islamic legal terminology it is defined as the total expenditure of effort by a mujtahid, in order to infer, with a high degree of probability, the rules of Shari’ah from the detailed evidence that is found in the sources.
Although all legal verdicts in Shiite jurisprudence is based on certain sources (Quran, Sunnah, reason and consensus), one needs to be able to derive Islamic laws from these sources. In order for him to gain competence in deducing laws, he must learn certain preliminary and pre-required sciences such as Arabic literature, Arabic grammar, logic, principles of jurisprudence, biographical sciences, knowledge of Quran and hadith. He should be cognizant of colloquial conversations in the time of the infallibles and should acquire knowledge of whatever is instrumental in deducing Shari’ah rules. Not only every faqhi (jurisprudent) should have acquired knowledge of these preliminaries but he should also have his own independent theories and principles in all these areas so that he can benefit from these sciences in deriving legal rulings.  For example, when it comes to making use of traditions and reports, a mujtahid who has adopted certain principles and procedures in ilm-e rijab (biographical science) may consider a tradition inauthentic and unreliable. He will not use it and that tradition could be the only tradition in a certain area. Thus, he cannot give a fatwa in that regard, whereas another mujtahid who considers the same tradition to be authentic and reliable uses it as reference to give a fatwa.
There is no doubt that different scholars have various degrees of competence and ability in sorting out and analyzing juridical issues. Therefore, every mujtahid may possibly have different understanding and perceptions of Quranic verses and traditions. As well, it is possible that a mujtahid might consider something to be the subject and manifestation of a specific ruling whereas another may not consider it as such.
Now for further explanation about the major sources of derivation of Islamic laws[3] (such as the Quran, Sunnah, consensus and reason) according to jurisprudents  we shall highlight some of the principles associated with each of the authoritative sources:
1.  The Holy Quran: The Quran is unquestionably the first and the most important source for derivation of Islamic rules. However, deriving Islamic laws and giving fatwa on the basis of any Quranic verses requires the jurisprudent to have his own view and standpoint in regards to the affirmative principles and basic questions: Are the in-depth and profound meanings and concepts of the Quran understandable or not? Have any distortions taken place in the Quran?[4]
2. Sunnah (sayings and conducts of the infallible):  Obviously, the validity and authoritativeness of Sunnah including the sayings, conducts and tacit approvals of the Messenger of Allah (S) do not need to be proved. In view of the explicit Quranic references, it is not difficult to substantiate them as they do not require an extensive discussion. Therefore, Muslims have clearly admitted the validity of prophetic traditions.[5] Likewise, the sayings, conducts and assertions of the infallible imams are also part of the Sunnah. Imamiyah scholars are of the view that the solutions provided by the Prophet (S) for the ummah and which he reiterated time and again is the “authoritativeness of the sunnah of the infallible imams” (AS)[6] because the Prophet (S) said that he left two weighty and precious things after him i.e. the Quran and progeny of the Prophet (AS).  He said that people would not be misled as long as they keep following them.[7] Hence, if it is proved that the Messenger of Allah (S) or the infallible Imams (AS) practically performed their religious duties in a special way or others performed their religious duties in a special way in their presence which was tacitly or practically approved and endorsed by them i.e. they practically approved their practice, it is then sufficient for a jurisprudent to rely upon it in his efforts to deduce an Islamic ruling.[8]
Questions such as, a) Can Sunnah restrict or limit the Holy Quran? b) Can a situation have any impact on Sunnah?[9] are the key and fundamental questions about which the mujtahid should have his own idea and opinion so that he may be able to derive Islamic rulings from the Sunnah.
3. Consensus (all out agreement of jurisprudents on an issue):  According to Shiite scholars, consensus is an authoritative means for deriving Islamic laws because it reveals sayings of the Prophet (S) and Imam (AS).  For example, if it is known that Muslims living in the time of the Prophet (S) had a specific belief or opinion without any exception and behaved in a particular way, which is a sign showing they have received it from the Prophet (S). Similarly, if some of the companions of the pure Imams (AS) had a unified approach, it is a sign indicating that they have taken it from their imam.  Certainly, such a consensus is valid and holds good, not because of the consensus itself but because it uncovers an infallible’s saying.[10]
4. Reason:  In the advanced teachings of Islam, nothing has been praised and valued as much as reason or the human intellect. The praise is due, mainly, to the fact that the human intellect is instrumental and has a key function in recognizing the truths as well as in discerning right from wrong in various ideological, individual and social aspects of human life. It is inferred from the overall evidence and arguments that reason is inherently authoritative as can be stated by Shari’ah.[11]
For this reason, since long time, the authoritativeness and reliability of reason has long been a well-known basis for derivation of Islamic laws among Shiite jurisprudents and scholars.[12] Hence, the authoritativeness of reason according to Shia means that if reason gives a definite decree, that decree is authoritative simply because of its being definite and decisive.[13]
The conclusion is that the jurist and mujtahid gives fatwa on the basis of these four sources while relying on their own independent principles and procedures.  Of course, it should be noted that the discussion regarding the principles and procedures is not restricted to what was mentioned above.
For further information in this regard, you are advised to read treatises written by Professor Hadavi Tehrani titled “Ta’ammulât Ilm-e Usul” (Contemplations in the Principles of Jurisprudence).

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