There are many different narrations which describe the manner which the Prophet Muhammad (ﷺ) ate food.
Learning the proper etiquette for eating at the table is important and these can be broken into three different categories. They are (1) Before eating, (2) while eating (3) after eating.
As you will shortly see, the Sunnah of eating are timeless and still relevant today.
As the Prophet Muhammad said “I was sent to perfect good character.” 
Sunnah or Etiquette of Eating
1. Begin with Purification (washing hands).
When the Prophet was in a state of Junub (being impure) he would perform wudu before eating. In another narration it mentioned that doing Wudu before and after eating increased blessings but these hadith are da’if (weak).
It was narrated from ‘Aishah that: If the Prophet wanted to eat when he was impure, he would wash his hands. 
Salmaan Faarisi Radiyallahu ‘Anhu says: “I have read in-the Tauraah, that performing wudu (washing the hands) after eating increases blessings. I mentioned this to Rasulullah Sallailahu ‘Alayhi Wasallam. Rasulullah Sallallahu ‘Alayhi Wasallam said: “Wudu before and after eating (washing the hands and mouth) increases blessings. (Da’if)” 
2. Start with saying Bismillah.
It was narrated that ‘Aishah said: “The Messenger of Allah (ﷺ) was eating food with six of his Companions when a Bedouin came and ate it all in two bites. The Messenger of Allah (ﷺ) said: ‘If he had said Bismillah, it would have sufficed you (all). When any one of you eats food, let him say Bismillah, and if he forgets to say Bismillah at the beginning, let him say Bismillah fi awwalihi wa akhirih (In the Name of Allah at the beginning and at the end).’” 
In Surah Al An’am verse 121 Allah gives clear instructions to be grateful and to declare Allah’s name before eating food.
وَلَا تَأْكُلُوا۟ مِمَّا لَمْ يُذْكَرِ ٱسْمُ ٱللَّهِ عَلَيْهِ وَإِنَّهُۥ لَفِسْقٌ ۗ وَإِنَّ ٱلشَّيَٰطِينَ لَيُوحُونَ إِلَىٰٓ أَوْلِيَآئِهِمْ لِيُجَٰدِلُوكُمْ ۖ وَإِنْ أَطَعْتُمُوهُمْ إِنَّكُمْ لَمُشْرِكُونَ
“And do not eat of that upon which the name of Allah has not been mentioned, for indeed, it is grave disobedience. And indeed do the devils inspire their allies [among men] to dispute with you. And if you were to obey them, indeed, you would be associators [of others with Him].”
3. Eating Using your right hand and start with the food nearest on your plate.
Umar bin Abu Salamah (May Allah be pleased with them) reported: I was a boy under the care of Messenger of Allah (ﷺ), and as my hand used to wander around in the dish, he (ﷺ) said to me once, “Mention Allah’s Name (i.e., say Bismillah), eat with your right hand, and eat from what is in front of you.” [Al-Bukhari and Muslim]. 
4. Siting on the floor.
And it was narrated that he said: “I eat as a slave eats and I sit as a slave sits.” 
I eat as the servant eats, and I sit as the servant sits. Verily, I am only a servant. 
5. Blessings of Eating Together.
Salim bin ‘Abdullah bin ‘Umar said: “I heard my father say: ‘I heard ‘Umar bin Khattab say: “The Messenger of Allah (ﷺ) said: ‘Eat together and do not eat separately, for the blessing is in being together.’” 
6. Eating With Three Fingers.
Ka’b bin Malik (May Allah be pleased with him) reported: I saw Messenger of Allah (ﷺ) eating with three fingers (i.e., the thumb, the index finger and the middle finger) and licking them after having finished the food. [Muslim]. 
7. Be grateful and do not to criticize food you are given.
Narrated Abu Huraira: The Prophet (ﷺ) never criticized any food (he was invited to) but he used to eat if he liked the food, and leave it if he disliked it. 
8. Giving good compliments when eating something you like.
Jabir (May Allah be pleased with him) reported: The Prophet (ﷺ) asked for sauce and was told that there was nothing except vinegar. He asked for it and began to eat from it saying, “How excellent is vinegar when eaten as sauce! How excellent is vinegar when eaten as Udm!” [Muslim]. 
9. Do not waste food.
Jabir reported: I heard Allah’s Apostle (ﷺ) as saying: The Satan is present with any one of you in everything he does; he is present even when he eats food; so if any one of you drops a mouthful he should remove away anything filthy on it and eat it and not leave for the devil; and when he finishes (food) he should lick his fingers, for he does not know in what portion of his food the blessing lies. 
10. Eat in moderation, don’t be excessive.
It was narrated that ‘Atiyyah bin ‘Amir Al-Juhani said: “I heard Salman, when he was forced to eat food, say: ‘It is sufficient for me that I heard the Messenger of Allah (ﷺ) say: The people who most eat their fill in this world will be the most hungry on the Day of Resurrection.’” 
11. Praise Allah and be thankful for the food you are given.
Anas b. Malik reported that Allah’s Messenger (ﷺ) said: Allah is pleased with His servant who says: Alhamdulillah (all praise be to Allah) while taking a morsel of food and while drinking. 
Some may see the Sunnah of the Prophet (ﷺ) and find it inconvenient to sit on the ground versus a table. Remember, these are just the practices of the Prophet (ﷺ) and if we wish to follow them in the same manner it would be mustahab (recommended) although not obligatory. Not sitting on the floor or eating food which falls on the ground will not be a sin for the believer. Rather these are humbling or virtuous acts.
Allah knows best.
 Shama’il Muhammadiyah Arabic reference: Book 27, Hadith 187
 Sunan Ibn Majah Hadith 593
 Shama’il Muhammadiyah English reference: Book 26, Hadith 178
 Sunan Ibn Majah Hadith 3264 Classified as Sahih (Darussalam)
 Riyad As Salihin Arabic/English book reference: Book 3, Hadith 740
 Narrated by Abu Ya’laa, 8/318
 Shu’ab al-Iman 5519, Grade: Sahih
 Ibn Majah Hadith 3287 classified as Hasan (Darussalam)
 Riyad As Salihin Arabic/English book reference : Book 3, Hadith 749
 Sahih al-Bukhari 5409 and Jami at-Tirmidhi 2031
 Riyad As Salihin Arabic/English book reference : Book 3, Hadith 737
 Sahih Muslim 2033 d
 Sunan Ibn Majah Hadith 3351 Classified as Hasan (Darussalam)
 Sahih Muslim 2734 a