A consolidation method is just a way to treat an entity during consolidation based on how much of it you own or control. It makes sense, if you only own 10% of an entity, and another entity has an asset recorded for the value of that investment, you would be overstating your value if you let it add up at 100%. The following are the most common methods you might see.
Subsidiary: Entity owned at >50%
The Subsidiaries financial statements are consolidated and eliminated. The Equity associated with the subs financial statements are eliminated against the Holding companies Investment in the sub. If the Sub is not 100% owned, the owned portion of Equity is eliminated and the unowned portion is reclassed to Minority Interest.
Equity: 50% >Entity owned >20%
An Entity held, as Equity Method is NOT consolidated. The Net Income of the Entity is multiplied by the Equity holding and the result is booked to the P&L and Equity Holding (Balance Sheet Equity Investment) of the Holding companies books.
Cost: Entity owned at <20%
An Entity held as Cost Method is NOT consolidated. The Net Income of the Entity is multiplied by the Cost holding and the result is booked to the Holding companies Balance Sheet in Other Investments. There is no P&L impact.
Acquisition and Disposal: Not a traditional method, but can be used as one
The entire P&L and Balance Sheet are each net to a single account on each statement. Usually the name of the account is something like "Income (or Loss) from Discontinued Operations" below Income from Continuing Operations and before Net Income. It represents the after tax gain or loss on sale of a segment of business and the after tax effect of the operations of the discontinued segment for the period. This method approach allows you to automate this calculation.
Holding Company: A special entity and not really a method
Holding companies hold the Investments of other entities. The Holding Companies Equity LIVES and is not eliminated until its parents equity is eliminated.