Hi C.,
Congrats on your new baby! I would suggest reading the book "On Becoming BabyWise" by Gary Ezzo, if you haven't already. This book absolutely saved me when my second child was born (with my first daughter, we spent a nightmarish first year where she slept no longer than 2 hours at a stretch - so with #2 I knew something had to change!)
Anyhow, the primary idea of the book is that if you have a schedule for eating, feeding and awake time, life will be a lot easier all the way around - your baby will know exactly what to expect and will not fight going to sleep. Sounds too easy to be true, but it works. What you can do first is make sure your baby is getting a good, solid meal at every feeding. This may mean that you'll have to take off her hat, take off her sleeper, maybe even take her diaper off so she is a little bit cold - whatever you have to do to keep her awake for the entire feeding. It's important that you do not allow her to fall asleep while nursing. Then after she is done eating, keep her awake for a little while. When it's time for her to sleep, put her down awake in her bassinet. Important: do not wait until she is exhausted to put her down! You can put her in there fully awake, and that's actually better. It's ok if she doesn't fall asleep right away. Remember that perfectly healthy and normal babies may cry a little bit - this may be one of the only ways they can get rid of stress, and it's ok to let them cry a little bit. (I'm not advocating crying it out at this age, simply saying that crying is not always bad.) Give her a pacifier if she likes them, so she can self-soothe with that.
At this point, you should be on a 3-4 hour eat-wake-sleep pattern. As she gains weight and gets older, this will increase and you'll find that she'll sleep through the night pretty early if you can get her to learn to self-soothe and go to sleep on her own. (My second child slept through the night at 1 month, which people will tell you is just luck, but it's not - it's scheduling feeding, waking, and sleeping.)
This is one of the most critical skills you can help your baby learn, and there does not have to be any crying it out. The most important thing is not to nurse her to sleep. I know that's probably contrary to what you may have been told at the hospital, but I promise you it works!
Best of luck to you and your darling new baby!