If you're reading about spring cleaning you probably try to keep your house in some kind of order, so it seems safe to assume that you have cleaning stuff on hand. But when you're doing some serious cleaning, you might need to invest in cleaners and tools that you don't usually have at the ready.
Despite what you see in the cleaning products aisle, you can actually get by with very few cleaners. It's all about your preference and what you need to tackle. There are lots of multi-purpose ones that can be used on floors, counters, walls and bathrooms. Often they can be diluted to various strengths depending on whether you are mopping or cleaning up a serious mess in the fridge. Some people prefer to use something with antibacterial properties for the kitchen and bathroom. Then you need something alcohol or vinegar based to clean glass, like mirrors and windows. A basic stain remover for carpets and upholstery is also handy.
Now we'll get into the more specialty cleaners. Dusting sprays are actually a no-no for wooden furniture -- they leave a residue, so get a paste wax. Countertops made of soapstone need to be oiled with mineral oil; granite or marble surfaces have their own special cleaners (regular household cleaners can damage them). Want to polish your silverware or copper pots? Yep, you need a special polish. Getting out a carpet cleaner? You can't just put any old soap in there. So figure out what you want to do, and then buy what you need.
Then there are the tools: broom, dustpan, mop, bucket, vacuum cleaner, cloths or sponges, dusters. Some people swear by feather dusters, but others claim they just spread the mess around and prefer microfiber ones. Also consider buying two buckets -- one for mopping and one to carry your supplies from room to room. If you have high ceilings like I do, you'll also need a step-stool or even an extension pole to get those cobwebs. Finally, gloves are always a good investment if you want to avoid touching muck or have sensitive skin.