• is a living human being
   
• is baptized
   
• has proper intent 
   
• has fasted the proper amount of time: 3 hours is the 1962 practice that most traditional Catholics follow (some follow the older practice of a 12-hour fast); 1 hour is what we are canonically bound to by the 1983 Code of Canon Law. Viaticum -- the "Food for the Journey" given during Extreme Unction -- may be given at any time.
     
• is in a state of grace, i.e., is not in a state of mortal sin. If one is in a state of mortal sin, he must go to Confession first lest he sin further as St. Paul warns in I Corinthians 11:26-30:

  
  
  Summary: one in grave sin is to police himself and refrain from receiving Communion until he's received the Sacrament of Penance. If he fails to, his spiritual father is to advise him in order to make him aware of his sin and of the added sin of receiving Communion while not in a state of grace. If, after being advised by his spiritual father, he still fails to police himself, he is to be prevented from receiving the Eucharist, especially if the grave sin is a public one.

The Eucharist must be received at least once a year, during the Easter Season, by those who've reached the age of reason, and shouldn't be received more than once a day (unless it is given as Viaticum during Extreme Unction).

The matter of the Sacrament itself are wheat bread made only of flour and water, with nothing added (no leavening, no honey, no spices, etc. -- nothing may be added) and wine fermented from grape juice. 

The former is confected by God through a true priest using the words:

This is My Body

Latin: Hoc est enim Corpus Meum.

The latter is confected by the words "this is the Chalice of My Blood," spoken in the below context in the Traditional Mass:
 

For this is the Chalice of My Blood, of the new and eternal Testament: the Mystery of Faith: which shall be shed for you and for many unto the remission of sins

Latin: Hic est enim Calix Sanguinis mei, novi et aeterni testamenti: mysterium fidei: qui pro vobis et pro multis effundetur in remissionem peccatorum.

The effects of receiving the Sacrament are:

• union, by love, with Christ
   
• an increase in sanctifying grace in the soul when received by a "living member of the Church" 
  (i.e., one who is in a state of grace)
   
• the blotting out venial sin and preserving the soul from mortal sin, in proportion to the communicant's devotion
   
• the rewards promised by Christ in His words, "He that eateth my flesh and drinketh my blood, hath everlasting life: and I will raise him up on the last day."

The proper way to receive the Blessed Eucharist at the altar rail at Mass is to kneel and fold one's hands in the "prayer" gesture (or place them under the houseling cloth at the altar rail, if such a cloth is used; don't touch the cloth or the rail in either case). An acolyte or altar boy will hold a paten underneath your chin so that no precious particles will fall to the floor. The priest will bless you by making a Sign of the Cross with the Sacrament (a small one in the air) and then place the Sacrament on your tongue, all while saying these words:

Open your mouth wide enough and stick out your tongue far enough to easily receive the Sacrament (once received, do not  respond "Amen" as is done in the Novus Ordo Rite). Most people make the Sign of the Cross after receiving Communion.