Symbolic meaning of the bread and wine
JW's do not accept transubstantiation (the unyeasted bread means/symbolizes Jesus' perfect and sinless body and the wine represents his blood he sacrificed to save humankind from the sinful state inherited by Adam). The biblical verses in the NWT, the translation JW's commonly use, also underline this symbolic meaning of the bread and wine. The wine and bread are thus considered symbols or emblems.
To answer your question properly, one has to understand the basic tenets of JW's doctrine.
JW's believe that throughout the entire Christian history God has selected only 144,000 to go to heaven to rule as kings and priests together with Christ. According to JW's it is God's holy spirit who convinces the individual that they indeed belong to the anointed class and have a heavenly call. Only with them Jesus has entered into a second covenant.
God's Kingdom will however also rule over the earth, which will also be inhabited by righteous ones (JW's and non-JW's).
Partaking of the emblems: doctrinal restrictions
Only the ones who belong to the 144,000 anointed partake of the emblems (i.e. eat from the bread and drink from the wine). Thus they show they belong to the second covenant and are one with Christ.
So in order to eat the bread and drink the wine in this day and age, you have to be (1) baptised as a Jehovah's witness and (2) believe you belong to the anointed class.
There are only a few thousands among the JW's today who still believe they go to heaven, the other JW's ("great multitude of other sheep") believe they will live for ever on paradise earth. So the great majority of Jw's do not drink from the cup of wine or eat the bread, but simply "pass" these emblems. Persons who are present at the memorial, but are no (baptised) JW's, are instructed not to partake of the emblems.
In most congregations of Jehovah's witnesses there are no anointed left, so the emblems are "merely passed" and left untouched.
Partaking of the emblems: time restrictions
The emblems are only passed once a year on 14th Nisan (last supper) and this to commemorate Jesus' sacrifice in accordance with his command (the memorial of Jesus' death).
The emblems are only passed and taken by the anointed after sunset. So the exact time (hour) varies from place to place, but the memorial can only be held when the sun has set.
Only when an anointed person is ill and can't make it to the memorial or there is another valid reason for his or her absence, the emblems can be taken on another date than 14th Nisan (this is very rare, and I take it the emblem must then still be passed after sunset in a kind of a private "ceremony").
Partaking of the emblems: age restrictions
The JW doctrine has undergone a substantial change recently. JW's believed since the 1930's that the number of anointed ones were "sealed". This normally meant persons had to be baptised as a JW before the 1930's, if they claimed to be of the anointed class. Since JW's are not baptised as infants, but later when they are personally convinced that their religion is true, normally only persons who are born in 1920's or before could belong to the anointed. I say "normally" because in theory a younger person could belong to the anointed class if an older anointed person defected from the faith and the younger one fills in the place among the anointed that has become vacant.
JW's now believe, however, that the number was never sealed in the 1930's, so every baptised JW could claim to belong to the anointed class. The only age limit is connected with the fact that the person has to be baptised. In theory an exceptional child which has sufficient understanding, say of 9 years old, could be baptised and thus partake of the emblems and claim an 'anointed' status. Such a decision would likely be highly controversial and probably met with some skepticism among JW's.
Partaking of the emblems: formalities
The red wine is poured out in a cup and the unyeasted bread leaves are laid down on a plate.
The passing and partaking of the emblems (cup and plate) happen while you remain seated. So one does not "go" to communion.
It also means there has to be a person to your left and to your right (you accept the emblem from the person next to you and pass it to the other). For the person at the end of the row of the seats, there is no one seated to accept the emblem. This problem is solved by men who are standing at the end of a row of the chairs who accept the emblem and pass it to the next row of sitting persons. Somewhat peculiar is that these 'standing' men also take their seat afterwards and pass the emblems among them, this time while sitting.
Note
The memorial is the only time that the ones who partake of the emblems are counted: in that way the JW's organisation still keeps track of how many persons of the 144,000 anointed ones still remain alive today (therefore they are called the "holy remnant").
These figures are published every year, together with other statistics.
The fact if you are anointed or not, does not have any other special effect (except that only anointed men are on the Governing Body).