The first thing you should do is check out what you have at home. Chances are you've got some pencils, pens, notebooks and crayons that are new or relatively new that would be a perfect addition to your child's school supplies. Also, things like rulers, calculators and backpacks don't necessarily need to be replaced every year. Look and see what you can find around the house before you hit the stores.
Shop around! Lots of stores offer items at a significantly reduced price just to get you in the door. These items are often referred to as "Loss Leaders." Check your weekly advertisements for Loss Leaders. After you're at the store, don't be tempted to grab other stuff. Get the Loss Leaders and get out.
Look for coupons online or in the newspaper.
Ask if a store will price match. If you've got flyers with prices and you want to save yourself some time and gas, it's worth a shot!
Don't take your children. It's hard to tell kids no when they see a pencil, notebook, backpack, etc. they can't live without. If they stay home and you do the shopping, there won't be any temptation to give in to their requests. Otherwise, take them but clearly establish ground rules regarding what will or will not be purchased. Maybe let them pick one special item. Alternatively, tell them they can use some of their own spending money for a special item.
Stick to your list. Once you're in the store, all those fun extras can be tempting. Hold firm to avoid overspending on non-necessary items.
Try the dollar store first. You can find lots of items there that might be on your lists.
Don't buy something just because it's less expensive. Consider the quality of some items. Pencils and erasers and crayons are inexpensive and easily replaced so generic items are the way to go there. However, backpacks and notebooks with durable plastic covers are probably the way to go so that you don't end up having to replace them within a few months. You want the items you purchase to last this year, and into next year, if possible.
Try to set a budget that you can follow. Make sure your kids understand that they need to help you stick to the budget so that everyone can get what they need to start the school year off right.
Team up with other parents. Look for bulk supplies at Costco or Sam's and purchase school supplies in bulk at reduced cost. Split the supplies up between you. This is extremely helpful if the children are in the same class.
Stockpile supplies. When you hit a store that is offering up to five notebooks for a penny each, buy the maximum, even if you only need two right now. Your kids will probably need them later this year, or next year. Or you could always donate them to needy kids.