How does a person become an incorporated business here in Alabama?

1) You simply file in a state (your state, AL, is as good as any) to create a corporation or limited liability company (LLC), then use the registation you get from the state to request a EIN (Employer Identification Number; a/k/a tax ID #) from the IRS. You can do all of this online. Just google "incorporate Alabama" and look for the government website; then google "IRS EIN" and look for the IRS's website.
2) Cost--varies by state, but $250 - $500 is a good estimate.
3) Taxes--we will assumme you create either an LLC (and that when you do, you select what will be called "disregarded" or "pass through" or "partnership" tax treatment) or an S-corporation (not a C-corporation), since those are best for independent contractors. If you do that, the income (or losses--i.e. if you end up spending more on the business than you take in, such as on buying new computer or phone equipment, printers, lights, office furniture, etc. to set up a home office, the surplus of costs over income becomes a business "loss" that gives you a tax deduction) "passes through" or "disregards" the business structure and goes right to your bottom line and is taxed with any other income (from any side or second job, or rental income if you rent out part of your home, etc.) you make. The business has no detrimental effect on your taxes and does not increase your taxes. In fact--and discuss this with a tax preparer or accountant--it may facilitate you deducting certain expenses as business expenses.
4) Whether to set up an LLC or a S-corp.: there really is almost nothing to chose between with these two structures for an independent contractor's purpses, except that an LLC involves a bit less paperwork and formalities; therefore, for an indepdent contrator, the LLC is probably better, or at least more convenient.