Let's start with the asset approach (and then focus on more important issues :-)

I'll start with the asset approach. It's the most basic one, but purely static. To simplify, you look at the current balance sheet of the company, and what's left after you deduct total liabilities from total assets is the value of equity. If you assume that book value of assets is equal to the market value of assets, then the book value of equity is also equal to the market value of equity. Usually, it's not.

Just to make it clear what I am talking about see this picture (in this example market value of equity is higher than the book value):

So, to start with the basic question: when to use this approach?

• You should use this approach for financial and real-estate holding companies.  
• You can also use it to estimate the liquidation value of any company.
• You should NOT use it to estimate the value of an »ordinary« manufacturing or services company, if such a company is a going concern. Why not? Because the asset approach assumes you sell all the assets, pay all the liabilities and what's left is shareholder's equity. If you do that, then it's no longer a going concern. For such a company, you then also need to take into account that you need to pay severance packages to workers, costs of selling these assets, costs of attorneys, accountants etc.

How to use this approach?

• You start with the balance sheet and identify all the assets and all the liabilities. Not all of them may be shown on the balance sheet (e.g. intangibles, such as trade marks, lists of customers; assets that are still in use, but are already wholly depreciated with book value = 0; potential liabilities from law-suits etc.).
• You estimate the market value of assets. You should pay a special attention to receivables (can they all be collected), inventories (what's their market value), financial assets, fixed assets (especially real-estate if held at purchase value), intangibles (some of it you cannot sell on the market or at deeply discounted prices, others are not identified in the balance sheet).
• You estimate the market value of liabilities (book value is in most situations a good enough estimate of the market value). Again, pay special attention to any potential liabilities not shown in the balance sheet.
• You deduct liabilities from assets, and what's left is shareholder's equity.

So, it's a fairly simple and straightforward approach, but with many caveats (as mentioned above). It's important to remember that market value of assets and liabilities may significantly differ from the book value, so don't assume book value is any kind of indicator of the market value!

How to...

There are three main approaches to valuing a business.
1. Market approach
You look at the value of similar companies as compared to some financial parameter (usually EBIT, EBITDA, net profit, sales, book value of equity etc.) and then apply this multiple to the financial parameter of the company you're valuing to estimate its value. A simple example:
Company A, which is very similar to company B that I'm trying to value, is worth 100 and has EBITDA of 10. The Value/EBITDA multiple is 100/10 = 10. Company B has EBITDA equal to 12. Using the multiple of company A we can estimate the value of company B to be equal to 120 (12 x 10).
2. Income approach
You prepare financial projections of the company for the future. You calculate free cash flowand estimate its present value. This is theoretically and practically the best and most appropriate approach to use, since it yields the most "correct" result (and we'll talk about getting to the "correct" result as well).
3. Asset based approach
The most static approach, useful only for holding companies or companies in liquidation. You estimate the value of assets (as if sold separately) and deduct the value of any obligations.

I'll go through these approaches into greater (but not too great) detail and also touch upon other topics (liquidity, minority vs. majority ownership stakes, valuation of start ups,...).

Feel free to suggest other, even more specific topics of interest that I can elaborate on with respect to business valuation and/or ask questions that I will try to answer.