How does regeneration work?

Although regeneration usually appears as an involuntary, biological process that occurs when death would otherwise be imminent, the nature of regeneration has not always been consistently represented. It has been most fully explored over the years in the case of the Master:

• It's possible to reset the counter on regenerations-- as in The Five Doctors (1983), when the Timelords offer the Master a new set of regenerations.
• Regenerations can be transferred from one Timelord to another-- as in the 1996 TV movie, when the Master attempts to steal the Doctor's remaining regenerations.
• A Timelord can decide whether to regenerate-- as in Last of the Timelords (2007), when the Master refuses to regenerate and (apparently) dies.
• The source of regenerative power is on Galifrey, and is associated with (possibly originates in) the Eye of Harmony-- as in The Deadly Assassin (1976) where the Master schemes to become Timelord president specifically to gain access to the Eye and avoid death at the end of his last regeneration.

However in all of these cases, the question of "how would that work, exactly?" is never answered.

While regeneration is commonly something that happens when death might be expected, it doesn't have to be this way:

• Romana regenerates in Destiny of the Daleks (1979) at will, just because she wants to do so. In the opening scene she apparently regenerates several times until she finds a look that she likes-- as if she were trying on new clothes.
• The Doctor's second regeneration (The War Games, 1969) was forced on him by the Timelords. They don't do anything that would be expected to kill the Doctor-- they just make him regenerate.

Romana's regeneration also suggests pretty strongly that the regeneration limit is not a major concern, since otherwise the repeated regenerations would be nearly suicidal. Whether this is because she thinks she can reset the count, or because the limit doesn't apply to her, or for some other reason is not stated.

From past evidence it therefore appears that:

• Regeneration is an inherent capability but one that can only be done a fixed number of times.
• The process involves some undefined energy carried by the individual which can be transferred or restored.
• The Timelords possess the power to transfer this energy (probably from the Eye of Harmony on Galifrey) and can therefore restore regenerative power.
• Timelords in good standing (like Romana) can get their "regeneration energy" replenished on request, or may simply be allowed to access the energy source and do so themselves.
• Timelords not in good standing (the Master and... sometimes.. the Doctor) may have this request refused (e.g. by being denied access to the Eye of Harmony).
• If you know what you're doing, you could transfer this energy from one individual to another, effectively giving one person the other's remaining regenerations. This was half confirmed in Let's Kill Hitler(2011) when River Song gave up her remaining regenerations to stop the Doctor from dying.

There is quite some information on this (mostly from the old series) if you google it so I won't give a full explanation but only my own interpretation. The regeneration process is a natural ability of the Time Lord race to regenerate completely when mortally wounded. Once the process starts, the cells of the Time Lord produce energy that can completely transform the body of the Time Lord. The energy production cannot be stopped but the tenth Doctor is shown to be able to guide it somewhat as he heals himself and direct the surplus of energy to his severed hand.

During the series, the limit of 13 incarnations of a single Time Lord is mentioned but this limit should not be taken so strictly. There are several episodes in which exceptions to this limit have been shown (the most recent being the regeneration of the Master). As far as I know, there have been no elaborate examples as to what would happen if a Time Lord were to regenerate over the limit. This could be a simple rule in their society (to avoid overpopulation) or really be a biological limit (cell deterioration after too many regenerations) but this is speculation. As the Doctor is nearing the limit, I believe that we will see more on this rule in the following season(s).