As with many other issues, the Bible does not say anything directly about contraception. However, as with the other issues, the Bible offers principles that can help us form our attitude to contraception: –
Sex is viewed very positively in the Bible. For example, God’s very first command to the first husband and wife (Adam and Eve) was “Be fruitful and multiply and fill the earth” (Gen. 1:28). And pro-creation is not the only positive purpose for sex within a marriage: the Bible emphasises that sex is something to be enjoyed with your spouse — the enjoyment of sex can help bind a marriage together:
{1} Now concerning the matters about which you wrote: “It is good for a man not to have sexual relations with a woman.” {2} But because of the temptation to sexual immorality, each man should have his own wife and each woman her own husband. {3} The husband should give to his wife her conjugal rights, and likewise the wife to her husband. {4} For the wife does not have authority over her own body, but the husband does. Likewise the husband does not have authority over his own body, but the wife does. {5} Do not deprive one another, except perhaps by agreement for a limited time, that you may devote yourselves to prayer; but then come together again, so that Satan may not tempt you because of your lack of self-control (1Cor. 7:1-5)
The Bible’s guidance that sex can be enjoyed in and of itself (without the necessity of it being for the purpose of pro-creation) lends to the use contraception. In fact, it would be irresponsible not to use contraception in some situations in marriage: if, for example, a couple could not support a child financially then it would be potentially irresponsible to not use contraception and risk bringing a child, whom they could not care for well, into world.
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Postscript
Sometimes the record of a man called Onan (Gen. 28:1-10) is used to try to prohibit the use of contraception. However, Onan’s sin was not that he used “contraception”, but that he did not ‘perform the duty of a brother-in-law…and raise up offspring for [his] brother’ (v8) — cf. Deut. 25:5-10.