Eastern Rite: Orarion, Epitrachelion
Whether you are talking about the orarion or the epitrachelion, both are a band of decorated or brocaded cloth.
Subdeacons and Deacons wear the orarion over their sticherion or dalmatic. The Subdeacon wears his around his waist, then over each shoulder forming an X across his back, and then bringing the orarion back over the shoulders to the front to tuck under the part already around his waist. (According to an Orthowiki article, some traditions may bless an ordained acolyte to wear the orarion, in which case it is worn in the manner of a subdeacon.)
(Above is an example of the subdeacon's orarion worn over the sticharion. Newly-ordained Subdeacon John Hogg stands with his father, Fr. Gregory, overlooking.)
The Deacon wears his orarion over the left shoulder alone, draping it straight downward. Among the Greeks the Deacon's orarion is longer and worn over the left shoulder and once around the chest to come back up to the left shoulder. This is called the double orarion. Among the Russians this looping method is bestowed as an award.
(Above is the single orarion worn over a simple yet lovely sticharion. Below is a deacon's dalmatic worn with the double orarion.)
Priests and Bishops wear the epitrachelion around the neck. It tends to be a wide cloth when viewed from the front. Often the epitrachelion is held together with buttons down the front, which gives the appearance of a single piece of cloth with a hole for the neck at the top.
(Above is an example of a typical epitrachelion.)
Western Rite: Stole
The stole is the same basic idea as the orarion and epitrachelion. It is a band of decorated or brocaded cloth. Some are wider, some are thinner, but all follow the same basic premise.
Subdeacons do not wear a stole in the Western Rite. Deacons wear the stole over the left shoulder, not vertically so but diagonally across the chest and back to cross at or near the opposite hip.
(Above is an example of a typical modern deacon's stole.)
Priests wear the stole around the neck, but it is not joined down the center as with the epitrachelion. Instead each side is brought together to form an X shape across the front.
(Above is an example of a typical priest's stole.)
Bishops wear the stole around the neck, too, but it does not join together in an X at all. Rather, each side hangs vertically.