What Does it Take to Issue a Fatwa?

What does it take to be a judge or to issue a fatwa? What does it take to be a Mujtahid Mutlaq (a scholar of Fiqh who is not restricted to a math'hab)? 

Imam Ibn Qudama (may Allah have mercy on him) summarizes this in his famous book, Al-Muqni, and much more details are mentioned in the books of Usul Al-Fiqh.
He says:
The Mujtahid is he who knows from the Book of Allah (the Most Exalted) and the Sunnah of His Messenger (praise and peace be upon him):
- Haqeeqa and Majaz (real vs. figurative speech)
- Al-Amr wan-Nahy (what is commanded and forbidden, and rules related)
- Al-Mujmal wal Mubayyan (what needs explanation and what is clear)
- Al-Muhkam wal-Mutashabih (what is clear in itself, and what is not clear)
- Al-Khaas and Al-'Aam (specific and general texts)
- An-Naasikh and Al-Mansookh (What is abrogated and what is not)
- Al-Mustathna wal-Mustathnaa minhu (what is an exception to the general rule, and the general rule)
And he should know from the Sunnah that is related to Fiqh rulings
- What is authentic and what is weak
- What is mutawatir and what is Aahad (not mutawatir)
- What is Mursal and what is Muttasil (Mursal vs. connected chain)
- What is Musnad and what is Munqati' (connected vs. disconnected chains)
He should know: 
- What is Ijmaa' and what is khilaaf (where scholars agreed and where they differed)
He should know Qiyas
- And its definition (and pillars)
- Its conditions
- How to correctly extract a ruling with it
He should know the Arabic language
- used in Hijaz, Sham, Iraq, and neighboring lands.

All of this is discussed (in detail) in the sciences of Usul al-Fiqh and Fiqh (and the science of Hadeeth). So whoever learns it and is blessed to understand it, then he is fit for being a judge and giving fatwa. And with Allah lies success.

Source: Al-Muqni' by Ibn Qudama

Al-Mardawi regarding the Mujtahid Mutlaq

A Mujtahid Mutlaq:
- Is the one has fulfilled all of the conditions of Ijtihad mentioned before.
- So, he is able to extract the religious rulings from Islamic evidences, whether general or specific, as well as the ruling of new issues that arise.
- He is not restricted to any specific math'hab

Al-Mardawi quotes Ibn Hamdan in Adab Al-Mufti wal-Mustafti, saying, "For a long time, there hasn't been a Mujtahid Mutlaq, even though it is now easier to reach than the earlier eras. This is because Hadeeth and Fiqh have been compiled, as well as what is related to Ijtihad, such as the ayat, narrations, Usul Al-Fiqh, the sciences of the Arabic language, and other [sciences]. However, the will power [of people] has become weak, and the desire [to reach such a level] has weakened. They neglected it and got tired of it. They did not understand in order to be able to attain it."

Then Al-Mardawi says, "A group of our later [Hanbali] scholars considered from this category [of Mujtahid Mutlaq] Shaykh Taqy-ud-deen Ibn Taymiyyah, may Allah have mercy on him. His way (i.e. methodology) in his fatwas and compilations does prove this."

Reference: Al-Insaf, Al-Mardawi, vol. 30, p. 384