The best advice anyone can give you is to take a look at your skill set, what you are really good at, and consult on those topics. You want to be able to take your work experience and use it to prove the claims you are going to make as a consultant. For example, if you are a recently laid-off VP of an automotive company, you are not going to offer consulting services to farmers on how to improve their crop turn out. You have to know what you are good at. One should clarify here that you don't have to consult on something that you did as a professional. If you have a passion for interior design, and people you know look to you for insight on redecorating, you could become an interior design consultant.
Once you decide what type of consulting you want to do, you are going to need to set your fees. There are a number of things that you need to consider when you are setting up your fees. First and foremost realize that your time is valuable and so is your knowledge. People are going to pay you for what you know and how you can help them. You don't want to be arrogant and charge $500/hour if what you have to offer doesn't back up the price. Be realistic on what it is you have to offer.
The next issue to think about when setting your fee is that you are no longer employed by someone else. There aren't going to be any benefits taken out of your pay. You need to consider the cost of you running a consulting business. The goal is for you to make money, not run yourself into a hole.
Once you have your fees established you need to think about marketing. Clients are not going to come looking for you, at least not until you are established. You are going to have to market yourself. Create or have a brochure created that explains your services. Get that brochure out to where the people you can help are. If you are offering quality consulting on the business process of a manufacturing plant, then spending time talking to people that collect baseball cards is not going to be the best use of your time.
Knock on doors, network, contact former clients you had before you laid off. There is no shame in that. The success of your consulting business is dependent on what you know. The opportunities for you to show what you can do are often tied to who you know.
You can start a consulting business tomorrow, as long as you know the type of consulting you are going to do. Have your fees set, market yourself, and talk to people you know.