Ways that the word "sin" has been used in the Bible:

The first time the word translated into "sin" in the bible (it is referred here as a thing or object):

Genesis 4:7
"If you do well, will not your countenance be lifted up? And if you do not do well, sin is crouching at the door; and its desire is for you, but you must master it."

The actual Hebrew word used here for sin:

chatta'ah or chatta'th-
1) sin, sinful
2) sin, sin-offering
a) sin
b) condition of sin, guilt of sin
c) punishment for sin
d) a sin-offering
e) purification from sins of ceremonial uncleanness
** Brown-Driver-Briggs' Dictionary

Exodus 20:20
And Moses said to the people, "Do not be afraid; for God has come in order to test you, and in order that the fear of Him may remain with you, so that you may not sin."

The actual Hebrew word used here for sin:

chata' (khaw-taw');
a primitive root; properly, to miss; hence (figuratively and generally) to sin; by inference, to forfeit, lack, expiate, repent, (causatively) lead astray, condemn:
** Taken from Strong's Hebrew Dictionary

chata'-
to sin, to miss, to miss the way, to go wrong, to incur guilt, to forfeit, to purify from uncleanness
a) (Qal)
1) to miss
2) to sin, to miss the goal or path of right and duty
3) to incur guilt, to incur penalty by sin, to forfeit
b) (Piel)
1) to bear loss
2) to make a sin-offering
3) to purify from sin
4) to purify from uncleanness
c) (Hiphil)
1) to miss the mark
2) to induce to sin, to cause to sin
3) to bring into guilt or condemnation or punishment
d) (Hithpael)
1) to miss oneself, to lose oneself, to wander from the way
2) to purify oneself from uncleanness
** Brown-Driver-Briggs' Dictionary

In the new Testament:

John 1:29
The next day he saw Jesus coming to him, and said, "Behold, the Lamb of God who takes away the sin of the world!

Sin: hamartia (ham-ar-tee'-ah);
derived from a(marth/sei hamartano; a sin (properly abstract):
** From Strong's Dictionary

hamartano-
1) to be without a share in
2) to miss the mark
3) to err, be mistaken
4) to miss or wander from the path of uprightness and honor, to do or go wrong
5) to wander from the law of God, violate God's law, sin
**From Thayer's Dictionary

hamartano (ham-ar-tan'-o);
perhaps from a(alpha) (as a negative particle) and the base of me/rh (meros); properly, to miss the mark (and so not share in the prize), i.e. (figuratively) to err, especially (morally) to sin:
** From Strong's Dictionary
a alpha (al'-fah);
of Hebrew origin; the first letter of the alphabet; figuratively, only (from its use as a numeral) the first:
** From Strong's Dictionary

meros-
1) a part
a) a part due or assigned to one
b) lot, destiny
2) one of the constituent parts of a whole
a) in part, partly, in a measure, to some degree, as respects a part, severally, individually
b) any particular, in regard to this, in this respect
** From Thayer's Dictionary