How does Christianity define idolatry?

First, "idolatry" is anything we cherish above God or is more important to us than the true God. Second, they are predominant beliefs or strongholds in the mind, thus these beliefs overtake the mind and become like gods or husbands in the soul. These thoughts are called 'husbands' because our thoughts are our closest companions. The Bible considers every belief to be a god or idol, thus, these beliefs replace the image and likeness of the true God in us. As Christians, it is clear in Scripture that we are admonished to meditate on God's Word, for this is where we discover God's virtues, character, and attributes.

Psalm 115:8

Those who make them [idols] become like them, as do all who trust in them.

Psalm 135:16-18

They [idols] have mouths, but cannot speak; they have eyes, but cannot see; they have ears, but cannot hear; nor is there breath in their mouths. Those who make them become like them, as do all who trust in them.

Isaiah 44:9-11

How foolish are those who manufacture idols. These prized objects are really worthless. The people who worship idols don’t know this, so they are all put to shame. Who but a fool would make his own god—an idol that cannot help him one bit? All who worship idols will be disgraced along with all these craftsmen—mere humans—who claim they can make a god. They may all stand together, but they will stand in terror and shame.

I think all denominations would generally agree that worshiping any type of idol as being idolatry. Which is the obvious, statues and objects which people bow before. However many denominations also consider certain material items and actions as a form of idolatry. Things that fuel self-centeredness, greed, gluttony, a love for possessions and ultimately rebellion against God.

Sources: http://www.gotquestions.org/idolatry-definition.html

What the bible says about idolatry: more here

Exodus 20:3
You shall have no other gods before me.

Deuteronomy 5:7
You shall have no other gods before me.

Exodus 23:13
Pay attention to all that I have said to you, and make no mention of the names of other gods, nor let it be heard on your lips.

Luke 16:13
No servant can serve two masters, for either he will hate the one and love the other, or he will be devoted to the one and despise the other. You cannot serve God and money.

Leviticus 19:4
Do not turn to idols or make for yourselves any gods of cast metal: I am the Lord your God.

Colossians 3:5
Put to death therefore what is earthly in you: sexual immorality, impurity, passion, evil desire, and covetousness, which is idolatry.

1Sa 15:23 For rebellion is as the sin of witchcraft, and stubbornness is as iniquity and idolatry. Because thou hast rejected the word of the LORD, he hath also rejected thee from being king.

Strong's Hebrew word translated Idolatry

H8655

תּרפים

terâphı̂ym

ter-aw-feme'

Plural perhaps from H7495; a healer; Teraphim (singular or plural) a family idol: - idols (-atry), images, teraphim.

Strong's Hebrew word translated iniquity

H205

און

'âven

aw'-ven

From an unused root perhaps meaning properly to pant (hence to exert oneself, usually in vain; to come to naught); strictly nothingness; also trouble, vanity, wickedness; specifically an idol: - affliction, evil, false, idol, iniquity, mischief, mourners (-ing), naught, sorrow, unjust, unrighteous, vain, vanity, wicked (-ness.) Compare H369.

Gen 31:34 Now Rachel had taken the images, and put them in the camel's furniture, and sat upon them. And Laban searched all the tent, but found them not.

2Ki 23:24 Moreover the workers with familiar spirits, and the wizards, and the images, and the idols, and all the abominations that were spied in the land of Judah and in Jerusalem, did Josiah put away, that he might perform the words of the law which were written in the book that Hilkiah the priest found in the house of the LORD. 2Ki 23:25 And like unto him was there no king before him, that turned to the LORD with all his heart, and with all his soul, and with all his might, according to all the law of Moses; neither after him arose there any like him.

In the Old Testament the Hebrew word for idolatry is translated often as image. The images are of false gods, busts, images of ancestors or sometimes of things shown to Moses from Heaven. It is important to remember the lesson from 1 Samuel 15:23 that stubbornness, idolatry and iniquity are all related. Stubbornness is universally understood but iniquity might cause some hindrance so I included its Strong's definition as well.

The earliest instance of idolatry in Christianity is the time Rebecka stole the idols of her father Laban. Various scholars disagree on why she stole them:

Pulpit Commentary

(Virg., 'AEn.,' 3. 148-150). Rachel's motive for abstracting her father's teraphim has been variously ascribed to a desire to prevent her father from discovering, by inquiring at his gods, the direction of their flight (Aben Ezra, Rosenmüller), to protect herself, in case, of being overtaken, by an appeal to her father s gods (Josephus), to draw her father from the practice of idolatry (Bazil, Gregory, Nazisnzen, Theodoret), to obtain children for herself through their assistance (Lengerke, Gerlach), to preserve a memorial of her ancestors, whose pictures these teraphim were (Lightfoot); but was probably due to avarice, if the images were made of precious metals (Pererius), or to a taint of superstition which still adhered to her otherwise religious nature (Chrysostom, Calvin, 'Speaker's Commentary ), causing her to look to these idols for protection (Kalisch, Murphy) or consultation (Wordsworth) on her journey.

New Testament View

Act 17:16 Now while Paul waited for them at Athens, his spirit was stirred in him, when he saw the city wholly given to idolatry.

Strong's Greek Word for Idolatry from Acts 17:16

G2712

κατείδωλος

kateidōlos

kat-i'-do-los

From G2596 (intensive) and G1497; utterly idolatrous: - wholly given to idolatry.

G1497

εἴδωλον

eidōlon

i'-do-lon

From G1491; an image (that is, for worship); by implication a heathen god, or (plural) the worship of such: - idol.

1Co 10:14 Wherefore, my dearly beloved, flee from idolatry.

Strong's Greek Word for Idolatry from 1Co 10:14

G1495

εἰδωλολατρεία

eidōlolatreia

i-do-lol-at-ri'-ah

From G1497 and G2999; image worship (literally or figuratively): - idolatry.

The New Testament also takes a similar approach defining idolatry as image/statue/anything physical worship.

Most modern Christians myself included believe you can make an idol out of anything which you prize more than God. Including a house, a dog, a car, a person, a grown up toy and etc anything which attempts to take your worship which should be directed at God can be an idol.