There are 3 main reasons why people incorporate: tax advantages, protection from liability, and the ability to divide the ownership and responsibility of a business (eg, partners, investors, etc).
Most small business are most concerned with taxes and liability protection, and will want to form a LLC or S-Corp. Although if you are not making much money it may not even make sense to incorporate.
If you do decide to incorporate, the entity you select will depend on which state you are in, how lucrative you anticipate the business will be, and whether you will have partners or not. I would defer to your accountant or lawyer. Keep in mind that a LLC can take an S-Election and be taxed like an S-Corp. LLCs are usually simple and flexible and can be a good choice for a hobby business. If you are starting a business that you know is going to produce a lot of money then an S-Corp could be the better choice. In my state, they are slightly more complicated than an LLC.
With that said, the basic idea is:
1. Select and form your corporate entity.
2. Obtain an EIN (don't obtain the EIN first - the EIN is tied to the business entity and you enter the business' information when applying to the IRS for the EIN).
3. Use the corporate docs and EIN to open up a corporate business account.
4. Sign contracts on behalf of the business - not personally.
5. Obtain any state or local licenses required.
6. Possibly also buy insurance at this point depending on what it exactly it is you are doing.
7. Make some money.
8. Run your business income and expenses through your business account. Keep this separate from your personal accounts.
9. Get fancy with payroll, employees, retirement accounts, etc once you are making some money
But before you do all of that, you want to make sure you have a viable business model. I think a lot of people get bogged down in the minutiae and then their businesses never go anywhere. Who cares if you have a LLC or an S-Corp if you don't make any money? That is where I would spend the bulk of my time. If the business is already making money then hire an expert to help with this. Every business at least needs a good accountant and their services are a write off.