It is very hard, and it will get easier. I found with ds2, I didn't pressure myself regarding sleeping through the night ( do not listen too much to those with the tales of their babies sleeping through - I'm not doubting them, I just don't think that's the norm!) Best thing you can do for your baby is be there when they need you, with the proviso that you need to look after yourself too. I would try one rest during the daytime, even if you can't sleep avoid rushing round, just lie in sofa with a book. It is hard to drift off quickly at night but you get better at it, and again if you're lying down it is still restful I think. Try to remember if you're giving your baby what they need, then you are doing a fantastic job. Getting them to sleep through is not the marker of success, not with a tiny baby!
Yeah that's the tricky thing! The whole 'you sleep when they sleep' thing is easier said than done! I find it really hard to drop off as soon as she does, and then by the time I do she's waking up again!
Thanks for all the replies. It's good to know what is normal. I am starting to find sleeping a bit difficult myself as i know i have so little time for it and really need to sleep immediately she does. Not easy!
Have you tried swaddling? My DD is 9 weeks old with a similar pattern to yours (so as far as I know it's normal BTW). We've been swaddling her for the past few nights and it seems to be making a difference!
Things you can try - feeding at least every couple of hours in the day. Keep day times (including naps) light, with noise going on around you and then keep night times dark and quiet, with as little talking or changing as possible.