Sulfur is generally the cheapest and gentlest way to do significant acidification without affecting anything else, although be aware it takes a year or so to have full effect. A little bit of sulfur goes a long way. Sulfuric acid is faster, although you have to be careful, both for your safety and your plants**; the more you dilute the acid, the safer you'll be, although the longer it'll take to acidify the soil. Ammonium-based fertilizers are also acidifying, but you have to be careful not to have too much ammonia in the soil at any point in time or you risk ammonium toxicity (I've lost plants to that
). Urea and anhydrous ammonia are acidifying, but not as much as ammonium compounds (per unit N). To the extent that your plants need phosphorus fertilization, you can use phosphoric acid; it's one of the safest of the strong acids, but you're limited by how much phosphorus your soil needs. Nitric acid is of course quite acidifying, but it's rather dangerous - not merely corrosive like sulfuric acid, but also with a tendancy to create toxic gases or explosive compounds when used improperly. Also, iron sulfate is acidic, although a rather expensive way to acidify soil. If of course does add iron, but unlike chelates, you won't get the iron benefits with iron sulfate until you get the pH down.
** - If you want to earn some respect for concentrated sulfuric acid's ability to eat away organics, pour some on some sugar
Concentrated sulfuric acid is like a flameless fire in liquid form. Always remember: pour acid into water, not water into acid!
If you don't want to pay for a detailed soil analysis (you probably only need to know pH), you can pick up a cheap soil test kit online. You can get either self-contained, multi-test ones that use a colour indicator that you match up with a colour chart; or single test ones that you mail in using a provided envelope, and they do a precise professional analysis (included in the cost of the kit)