The argument against artificial contraception (eg: pill, coil, barrier methods etc) is that it prevents conception from taking place at all - therefore stopping life before it begins. Catholics believe that life begins from the second of conception (hence the arguments against abortion and the morning after pill) and that all sexual encounters should be open to the possibility of conception taking place - it is not our place to deny life from forming at any stage pre- or post-conception only God can do that.
Obviously, not all encounters are open to conception, because of the woman's cycle, so the church actively encourages natural methods of contraception like the Billings Method, or use of a Persona machine to plan your family. Marriage vows include the vow to "...accept children lovingly from God..." and this means not using contraception and accepting that natural planning methods are not as effective as artificial ones.
I am no theologian, so I hope I've not made any silly mistakes here but the above is the Church's opinion as I understand it - I'm happy to be corrected if I've made any errors!
Incidentally, I have one child and am pregnant with my second. (I have been married for eight years and lost four babies through miscarriage). Pregnancy is fraught for me, both with danger to the baby and danger to my own health but I firmly believe that God watches over us and that He doesn't give you more than you can cope with. If I'm pregnant, it's because that child is meant to be and who am I to interfere with that?
Saying all this - I firmly believe that it is not my place to judge others and I think that everyone has to square their own circumstances and beliefs with their own conscience and that if anyone has chosen to use contraception, or do anything else that gose against the teaching of the church, then that it's between them and God.