The Bible makes very few mentions of homosexuality - lesbianism isn't mentioned at all in the Old Testament - and as the examples below show, interpretations of the verses that do exist differ hugely.
Following each of the verses below is a brief illustration of what a hardline pro- and anti-gay position might be. (Most Christians hold views somewhere in between these two stances.)
An illustration of the division can be seen by what either side might say about the friendship in the Old Testament between David and Jonathan. One verse reads: "I grieve for you, Jonathan my brother; dear and delightful you were to me; your love for me was wonderful, surpassing the love of women."
A pro-gay position might be that this is a clear indication that King David had a gay relationship, and to pretend otherwise is naive.
An anti-gay opinion might be that the friendship between the two men was exactly that - a very close and loyal allegiance.
Similarly, the tale of Sodom is often debated. In it, Lot has two angels staying in his house. The men of Sodom surrounded the house. "They called to Lot and asked him where the men were who had entered his house that night. 'Bring them out,' they shouted, 'so that we might have intercourse with them.'"
To protect his visitors from an act which Lot describes as "wicked", he offers the crowd his two virgin daughters instead. The crowd are not satisfied and break the door down - the angels then make the intruders blind and Sodom is eventually destroyed by "fire and brimstone".
An anti-gay argument might say this story demonstrates the immorality of homosexuality, as has been accepted for generations, hence the term sodomy. Elsewhere in Genesis, God says of the men: "Their sin is very grave." It's an example of behaviour degenerating.
Of course the men's behaviour was wicked, but it was wicked because it's a tale of sexual assault and rape. When Jesus mentions Sodom, hundreds of years later, it appears to be in a context of a discussion of hospitality, rather than one of sexual morality.
There are several verses in the Bible which are similarly contested - there are however a much smaller number of seemingly clear statements. The most famous of them is probably from Leviticus: "You shall not lie with a man as with a woman; that is an abomination."
An anti-gay position would be that this line is unambiguous. It is also repeated elsewhere in the book. The speaker of the words is God, so this is an explicit indication that homosexuality is wrong in God's eyes. It was one of the sins that justified God in giving the land of Canaan to the Israelites
A pro-gay argument might say that other verses in the same book forbid a wide range of sexual activities, including having sex with a woman who is having her period. This is an indication that the passage embodies specific cultural values rather than God's law.
There is some debate about how relevant rules in the Old Testament are to Christians. Some would say they are binding, since Jesus said he did not come to abolish the old laws. Others would say that Jesus set Christians free from the old laws, highlighting instead that people should love God and their neighbour.
Jesus himself says nothing explicitly about homosexuality. There are though two statements by him which have been interpreted as having a bearing on the subject.
"[A] man shall leave his father and mother, and be made one with his wife; and the two shall become one flesh."
This indicates Jesus saw heterosexual relations as the proper way of behaving.
Jesus is actually talking about the sanctity of heterosexual marriage
Later in the same conversation, after Jesus has spoken about divorce, the disciples say to him it is better not to marry at all. Jesus says: "That is something which not everyone can accept, but only those for whom God has appointed it. For while some are incapable of marriage because they were born so, or made so by men, there are others who have themselves renounced marriage for the sake of the kingdom of Heaven. Let those accept it who can."
This shows that Jesus is more concerned with people looking after their own relationship with God, than with enforcement of rules. The reference to being "born so" indicates that heterosexual marriage is fine for those who are heterosexual, but it's OK to be different. Again and again Jesus reaches out to those on the margins of society, like prostitutes and tax collectors, to include them.
Jesus here is actually talking about people who were born incapable of having children, or people who were castrated - not about gays. He is actually saying that marriage and chastity are both within God's purpose. Jesus does appeal to the sinners, but once he has called them, he tells them to go and sin no more.
The letters of St Paul provide the other traditional support for the position that homosexuality is sinful. He writes: "God has given [people who worship false gods] up to shameful passions. Their women have exchanged natural intercourse for unnatural, and their men in turn, giving up natural relations with women burn with lust for one another; males behave indecently with males and paid in their own persons the fitting wage of such perversion."
Paul later writes: "Make no mistake: no fornicator or idolator, none who are guilty either of adultery or of homosexual perversion, no thieves or grabbers of drunkards of slanderers or swindlers, will possess the kingdom of God."
A pro-gay position might be that the word Paul uses for homosexual here could alternatively be translated as "male prostitute". In any case, Paul's writings are clearly of his time, and there are plenty of other verses which people have no difficulty in ignoring - for instance: "a woman brings shame on her head if she prays or prophesies bare-headed; it is as bad as if her head were shaved." This should be viewed like that.
Anti-gay argument might say this line is crystal clear in establishing that Christianity and homosexuality are incompatible. Paul is actually quite clearly referring to homosexual behaviour, and includes lesbianism. You can't just pretend that St Paul, who did so much to influence our understanding of Jesus, didn't know what he was talking about. He's clear that homosexuality is an offence against God and against people's own bodies.
Part of the reason the views diverge so much is because Christians think of the Bible differently. Some see it as literally the word of God, divine inspiration which humans should not question. Others see it rather as a book which is a witness to God's message, but one which was written by humans and thus has flaws.
Trying to find common ground between the two positions is no simple matter - one of the reasons that Dr Rowan Williams, the Archbishop of Canterbury, is having such a tricky job keeping everyone on board.