I cut back a lot with my son - I found that most things people were buying were just a waste of money. Examples: I never bought a change table. Instead I bought a low dresser (second hand) and put a change pad on top. I used one drawer for diapers and wipes and such and the other drawers for his clothes.
Another waste for me was a diaper genie or similar contraption. I found that they didn't keep the smell out as much as I would have thought and quite frankly it wasn't that hard to just chuck the diapers in the garbage can outside if they were smelly. Mine ended up breaking anyways, and I don't plan on replacing it for this baby.
I try to stock up on diapers and wipes when they are on sale. Here in Canada I buy my wipes at Costco because they are good and extremely cheap.
I also save a lot on clothes. We have a lot of family so my son gets lots of clothes for his birthday and Christmas, plus there were lots of hand me downs from cousins. When he was first born I wanted to buy him so much, but I learned quickly that the young babies in particular out grow their clothes so fast that quite frankly it is a waste to buy too much. It is so tempting at first to buy all the cute stuff and dress them up, but all those clothes add up and it just isn't worth it. Once they get older things last longer size wise so you need to have lots more, but when they are little you can get away with not buying much.
One more tip: regarding gifts - when it comes to Christmas and birthday gifts, when they are one or two they really don't understand what's going on. We all want to spoil our kids and buy them lots of stuff, but my advice is to hold back the first couple years if money is tight. Honestly, this past Christmas was my son's 3rd Christmas and I spent about $100 total on him this year. He got a couple big toys he had really wanted and a few small ones. It was more than enough to put a smile on his face and make it a happy day. Sure I could have spend $500 and spoiled him, but if you give them too much they are overwhelmed and won't play with everything anyways. This way I saved money that I can use during the rest of the year for things like swimming lessons, soccer, and trips to the zoo and other places.
Those are just a few of the things I have learned. When we first had out son we were pretty broke and had to get creative. Now we are much better off financially, but I've learned not to waste money.