How are Roman Catholics to receive the holy Eucharist at Mass? What is the etiquette to be followed when receiving the holy Eucharist? Is one to kneel down? Does one receive in the hand or directly on the tongue? Are there any prescribed procedures from Vatican?
In the US, what are the guidelines on how one should receive Holy Communion?


  Those who receive Communion may receive either in the hand or on the
  tongue, and the decision should be that of the individual receiving,
  not of the person distributing Communion. If Communion is received in
  the hand, the hands should first of all be clean. If one is right
  handed the left hand should rest upon the right. The host will then be
  laid in the palm of the left hand and then taken by the right hand to
  the mouth. If one is left-handed this is reversed. It is not
  appropriate to reach out with the fingers and take the host from the
  person distributing.
  Source: The Reception of Holy Communion at Mass | USCCB.



For the Holy See's position, please see: Communion received on the tongue and while kneeling | Office for the Liturgical Celebrations of the Supreme Pontiff.



  The most ancient practice of distributing Holy Communion was, with all
  probability, to give Communion to the faithful in the palm of the
  hand. The history of the liturgy, however, makes clear that rather
  early on a process took place to change this practice.
  
  From the time of the Fathers of the Church, a tendency was born and
  consolidated whereby distribution of Holy Communion in the hand became
  more and more restricted in favor of distributing Holy Communion on
  the tongue. The motivation for this practice is two-fold: a) first, to
  avoid, as much as possible, the dropping of Eucharistic particles; b)
  second, to increase among the faithful devotion to the Real Presence
  of Christ in the Sacrament of the Eucharist.
  [...]
  In continuity with the teaching of his Predecessor, starting with the Solemnity of Corpus Christi in the year 2008, the Holy Father, Benedict XVI, began to distribute to the faithful the Body of the Lord, by placing it directly on the tongue of the faithful as they remain kneeling.







For the history of Holy Communion in the hand please see: Library: Holy Communion in the Hand? By Paul Kokoski | Catholic Culture.
Please see also: Communion in the hand: Documents and History | Most Reverend Juan Rodolfo Laise, Bishop of San Luis, Argentina.
Please see this video: Make Of Our Hands A Throne. Typical reception of Holy Communion in the US. (OP: withholding comments).




Endnote


It is important to note that no bishop or bishop conference decide on their own what manner Holy Communion should be received by the Faithful. They must first petition the Vatican for an indult and a concession be granted. cf. Communion-in-the-Hand | EWTN.
For the communicant, the reception of Holy Communion by whatever manner that is approved in their own diocese ought to be done with the right and proper reverence due to the One being received. In my diocese the Bishop asks that the communicants bow before receiving Holy Communion, which they do standing.
@AndrewLeach has shared "The practice [...] of not handing the chalice to each communicant is actually laid down in the General Instruction of the Roman Missal." This is something not observed in my parish and therefore worth investigating further.