Following Islamic Eating manners; 

Washing mouth after drinking the milk, supplicating after finishing the food, giving starting from right.

Islam tells us that we should accept the food and drink wholeheartedly, be clean while we are eating, have a sense of goodmanners while we eat and thank the Almighty for all that has been bestowed upon us. The Prophet of Islam has mentioned that during ordinary times also, we can obtain reward. So also we are to receive the milk, finish our meal of eating and distribute food or drinks among people. 

These simple Sunnah actions ensure that a Muslim continues to keep the habit of thanking God even in common everyday actions; in fact these habits also become an avenue for us to practice remembrance of Almighty during eating and drinking of something which is a blessing in many different ways.

Washing our Mouth after drinking Milk:

Milk is indeed food which consists of numerous benefits; and apart from that it is also from the list of all that the Almighty had given us. A Sunnah action mentioned specifically is the action after we have had our milk. Ibn Abbas R A has narrated that Prophet Muhammad S.A.W. Drank milk and then washed his mouth. Prophet Muhammad S.A.W declared that milk had some fat in it.
A narration from Ibn ‘Abbas (RA) says: The Messenger of Allah (peace and blessings be upon him) drank the milk, then rinsed his mouth out. He then said: It has some of fat on it. (Sahih al-Bukhari 211)

In this simple action, a Muslim fulfills the obligation of taking care of the mouth and keeping it clean at all times, remembering the command of the Prophet. There can often be some residue left from the milk, and washing the mouth removes it easily. In such simple everyday acts, Muslims should also remember that their religion expects them to have goodmanners. They can even add this to their daily routines, when they drink milk.

Making Supplication after Finishing the meal:

Another practice followed during having food and drinking in Islamic tradition is making supplication and reminding ourselves of the Lord after the food is served and cleared away. Abu Umamah (RA) related that when he was clearing the diningspread after a meal, the Prophet Muhammad S.A.W had made a supplication of following nature; 

'Alhamdulillah-i katheeran tayyiban mubarakan feehi,ghaira makfiyyin wal-a muwaddada wal-a mustaghniya 'anha Rabbana.

" Meaning, 'O Allah, praise is due unto Thee - abundant, pure, blessed praise-no praise ever fully compensates Thee, nor may it be rejected, and we can not turn our backs on it, O our Lord.'

Narrated by Abu Umamah (RA): When the dining spread was cleared after the Prophet Muhammad (peace be upon him) ate food (or whenever that could be), there would be this saying of remembrance by him:All praise is due to Allah-abundant, pure, and blessed praise; praise that is never-ending, never to be abandoned, and indispensable, O our Lord. (Sahih al- Bukhari 5458)

This supplication signifies our eternal thanks giving to the One who gives food, health and other means. Muslims should always be reminded of having food and drink as Allah's bounty. The feeling of thanks that stems from reciting this supplication can truly change our whole day and even our perspective toward worldly necessities.

Give Starting from the Right side.
When foods or drinks are provided, a generally prescribed Muslim habit is to begin serving and the people are to receive starting from the right hand; for that part the has an additional status that it the first to receive something from anyone or whatever that is given. Anas bin Malik (RA) narrating from Abu Bakar (R.A) described what has the Prophet (S.A.W) narrated on this occasion:
Abu Bakr (RA) said: He then turned the place of a Bedouin man who was at his left hand towards his right hand, and this man then drank from that milk, then he gave the remainder to the man next to him to his right. (He gave saying): Take hold of it, the right, the right.
This Islamic Sunnah is followed at all times. When things like drinks etc are served among people this way it goes towards the right instead.

The rationale is to always give priority to right side.

Reasons and wisdom behind following these Sunnah practices?

1) CLEANLINESS: Washing hands properly before eating etc. Rinsing month after drinking milk is important to wash off any residues that milk has from having an oily property, to enable a muslim to not fall ill.

2) GRATITUDE: By always thanking Allah and asking for His favors over and over again helps to appreciate all the things that the muslim has. Thankfulness removes selfishness, materialism.

3) POLITENESS AND EXCELLENCE. Teaching humans how to treat other people with respect and dignity. Goodmanners, when eating and drinking the most required thing would be a clear example as the meal could be attended by family, friends, colleagues and others so by practicing etiquette.

4) Mindfulness, that what we consume is from Allah, and we should eat only from a permissible means and also remember Allah. We should never waste or underestimate any food given by Allah.. We should strive to consume good health promoting food from allowable means only; and give and eat according to Sunnah.

Conclusion

Islamic etiquette of eating offers numerous practical tips applicable to ordinary situations including what to say, when to say and how to act whilst having a meal. 

These Sunnah actions, namely rinsing mouth after consuming a drink of milk, uttering a supplication after finishing a food meal, and offering and receiving everything with an order of starting from the right, provide guidance for Muslims when they are experiencing their provision from Allah.

 While these may appear quite minor but the consistent application of Sunnah at all times can help people stay rooted in thankful heart, considerate of others, and always aware of God's abundant provision. 

The sincere observance of Sunnah by Muslims will result in following the noble example of Prophet Muhammad (Peace and Blessing be upon him) and in turning a normally mundane event into an honorable act of devotion.

Reference: Sahih al-Bukhari 211, Sahih al-Bukhari 5458, and the narration of Anas bin Malik (RA) for giving started from the right.

This is only for Islamic knowledge informations not for hurting others