First of all congratulations on the imminent birth of your child!

The answer to your question comes in three parts: short-term, middle-term, and long-term costs. If you think in these terms, the enormous costs of rearing a child become a bit more manageable. Some you will need to save for, some will come out of wages (so keep building your earning-power), and some you may need to borrow for.

Short-term expenses involve all the gear you need to welcome a child. Essentials include a good car seat (which will need replacing 2-3 times as the child grows), a baby carrier, a small cot, a crib, a playpen, a stroller, and high chair. If you walk into Babies R Us, there will be thousands of other things that you will think you "need," but if money is tight, keep your focus. Many of the essentials can be had second-hand. Yard sales are a great place to find them.
I would, however, recommend, that you buy some things new: the car seat, for instance, and the baby's sleeping gear.

As for mid-term expenses, the Department of Labor estimates that it costs as much as $250,000 to raise a child until age 18. This estimate includes housing which is not necessarily an "extra" expense, unless you need a bigger house because of your larger family. This seems like a lot, no doubt, but if you break it down over the eighteen years, it comes out to about $18000 a year before taxes. Use that number to motivate you upward in terms of your career. In this case, don't plan just for the baby, but start career planning for yourself.

The long-term costs involve college or university expenses. These, too, are huge, but the good news is that there are a lot of ways to pay for college, not all of which require additional savings on your part. Your child may be eligible for loans, grants, or scholarships. If you do want to contribute, use a 529 plan, as suggested, where the investment can grow tax-free, if used for approved college costs. For more info, go to www.savingforcollege.com.