Description of the Funeral Prayer
All praise is due to Allah, the Lord of all creation. May Allah's salah and salam be upon the most honourable of the Prophets and Messengers.
The funeral prayer is legislated for all, men and women. The Prophet (may Allah's salah and salam be upon him) said, "Whoever attends a funeral until the prayer is offered will have a Qirat, and whoever attends until the deceased is buried will have two Qirats." It was said, "O Messenger of Allah, what are the two Qirats?" He said: "Like two great mountains." This was reported by al-Bukhari.
Likewise, he (may Allah's salah and salam be upon him) said, "Whoever follows the funeral of a Muslim out of Iman and seeking Allah’s reward for it, and is present until the prayer is offered and burial is completed, will return with two Qirats, each Qirat like Mount Uhud." This was reported by al-Bukhari and Muslim.
Ruling of the Funeral Prayer:
It is a fard kifayah (communal obligation). If some perform it, the obligation is lifted from the rest. However, it is Sunnah for a large congregation to offer the prayer. The Messenger of Allah (may Allah's salah and salam be upon him) said, "Any deceased Muslim for whom forty men – who do not associate anything with Allah – pray over, Allah will grant them intercession for him." This was reported by Ahmad and Abu Dawud.
In another narration, he (may Allah's salah and salam be upon him) said, "No Muslim dies and a group of people numbering a hundred pray over him, all interceding for him, except that their intercession will be accepted." This was reported by Muslim and at-Tirmidhi.
Conditions of the Funeral Prayer
The intention, due to the Prophet’s (may Allah's salah and salam be upon him) saying, "Actions are judged by intentions." Facing the Qiblah, covering one’s 'Awrah (different for men and women), removing minor and major impurities, and ensuring cleanliness of prayer area and one’s garments. 
Description of the Funeral Prayer
Firstly: The Imam stands at the head of the deceased if he is a male and at the middle of the deceased if she is a female as mentioned in the hadith of Samurah ibn Jundub. It is reported from Anas ibn Malik (may Allah be pleased with him) that he prayed over a deceased man and stood at his head, and he prayed over a woman and stood at her middle. He mentioned that this was the practice of the Messenger of Allah (may Allah's salah and salam be upon him). This was reported by Abu Dawud and at-Tirmidhi, who graded it Hasan. In addition, it is reported that Samurah ibn Jundub said, "I prayed behind the Prophet (may Allah's salah and salam be upon him), and he prayed over Umm Ka’b, who died during childbirth, and the Prophet stood at her middle." This was reported by al-Bukhari and Muslim.
Secondly: He is to pronounce four takbirat (i.e., saying Allahu Akbar) due to the hadith of Jabir ibn ‘Abdillah (may Allah be pleased with him) in which he said, "The Messenger of Allah (may Allah's salah and salam be upon him) prayed over an-Najashi the king of Abyssinia, and pronounced four takbirat." This was reported by al-Bukhari and Muslim.
Standing during the funeral prayer is an obligatory pillar for those able, by consensus of the scholars.
It is from the Sunnah to raise the hands to shoulder level with each takbir.
1. He begins the prayer by pronouncing the first Takbir, by saying "Allahu Akbar." Then, he seeks refuge with Allah from the accursed shaytan, and recites al-Fatihah. He does not recite the opening du’a, as this prayer is meant to be light and easy.
2. Then, he says "Allahu Akbar" for the second Takbir, invokes Allah to confer salah upon the Prophet (may Allah's salah and salam be upon him): "O Allah, send blessings upon Muhammad and upon the family of Muhammad, as You sent blessings upon the family of Ibrahim. You are Praiseworthy, Glorious. O Allah, bless Muhammad and the family of Muhammad, as You blessed the family of Ibrahim - and made that known  among all of the creation. You are indeed Most Praiseworthy, Most Glorious.  
3. Then, he says "Allahu Akbar" for the third Takbir and supplicates for the deceased with the reported supplications: 
(اللهم اغفر لحينا، وميتنا، وشاهدنا، وغائبنا، وصغيرنا، وكبيرنا، وذكرنا، وأنثانا، اللهم من أحييته منا فأحيه على الإسلام، ومن توفيته منا فتوفه على الإيمان)
 "O Allah, forgive our living and our dead, those present and those absent, our young and our old, our males and our females. O Allah, whomever You cause to live, make him live upon Islam, and whomever You cause to die, let him die upon Iman." This was reported by at-Tirmidhi.

(اللهم اغفر له وارحمه، وعافه واعف عنه، وأكرم نزله، ووسع مدخله، وغسله بالماء والثلج والبرد، ونقه من الخطايا كما ينقى الثوب الأبيض من الدنس، اللهم أبدله دارا خيرا من داره، وأهل خيرًا من أهله، اللهم أدخله الجنة، وأعذه من عذاب القبر ومن عذاب النار)
"O Allah, forgive him, have mercy on him, pardon him, and grant him well-being. Honour his resting place, expand his entrance, wash him with water, snow, and ice, and cleanse him of sins as a white garment is cleansed of dirt. Replace his home with a better home, and his family with a better family. Admit him into Paradise and protect him from the punishment of the grave and the punishment of the fire." This was reported by Muslim.

Likewise, he may add to that: 
وافسح له في قبره، ونور له فيه، اللهم لا تحرمنا أجره، ولا تضلنا بعده، واغفر لنا وله

Make his grave spacious for him and illuminate it for him. O Allah, do not deprive us of his reward, do not lead us astray after him, and forgive us and him. 
Also, one may add to that:
اللهم إن كان محسناً فزد في إحسانه، وإن كان مسيئاً فتجاوز عن سيئاته
Allah, if he was righteous, increase his righteousness, and if he was sinful, pardon his sins. 

Or:
اللهم اغفر له وثبته بالقول الثابت
Allah, forgive him and make him firm with the firm statement.

The aforementioned supplications or any similar good ones are recommended. 

4. Then, he says "Allahu Akbar" for the fourth Takbir, pauses briefly, and then concludes with one Taslim.
This is what is authentically reported from the Companions of the Prophet (may Allah's salah and salam be upon him). The Islamic legislation is general for men and women in the prayer, but attending the burial and visiting the graves is specific to men.
Allah legislated the funeral prayer and following the deceased for the benefit of the deceased through supplication, consoling the bereaved, remembering death, and preparing for what comes after. May Allah grant us safety and well-being.