How does a battery recharge?

The method of charging a battery while being effective but without doing damage varies with battery chemistry.

Since you have a "12V" battery, I'm guessing it is a lead-acid type like you find in cars. Lead acid are fairly forgiving in how they can be charged, unlike other chemistries, especially certain types of lithium. Basically charge a lead acid with power that is both current and voltage limited. The voltage limit is usually 13.6 V for car batteries. The maximum current depends on the size of the battery. A ordinary car battery can take several amps easily. For example, a power supply that is limited to 5 A and 13.6 V will work just fine to charge ordinary car batteries, although that's not pushing the maximum allowed current. That means it will drop the voltage to not exceed 5 A or drop the current to not exceed 13.6 V, whichever is lower. Hardware and automotive stores sell chargers for car batteries that have all this built in. The only gotcha is a charger advertized as "fast" may abuse the battery. A full charge should take a few hours, although most of the time the battery should not get low enough to require that.

If your battery is smaller, then you have to dig up its datasheet or somehow get specs for it and make sure the charger doesn't produce too much current.

If your battery is not lead-acid, then things could be quite different. In that case you really have to get the specs, which should include the required charging profile. Getting this wrong, particularly with some types of lithium, could result in pyrotechnics.

batteries are source of electrical power and this power is characterized by two things Voltage(volts) and Current(amperes) now when you give a close look at the battery (in this case 12V) then what it means is that the battery can Provide a maximum Potential Difference of 12V between its Contacts.. there is also a Power rating available with the same.. a Cellphone battery may read 1300mAh@ 3.2V which means that the battery can supply 1300mA current for 1 hour at 3.2V. The chemicals inside the battery undergo some reaction and Produce a potential difference, the reaction stops at a particular Potential Difference, a voltage above which the reaction cannot proceed (in your case it is 12V) although it does not imply that the battery is weak! as you draw power from the battery you provide a way for these electrons to move out from one end and reach the other terminal thus providing a way for the reaction to occur, the reaction continues till the time any power consuming device is connected to the terminals and the chemicals are being used up in the reaction. when the battery is depleted it is identified by falling terminal voltage in your case the voltage levels shall fall below 12V.

now comes charging: during charging we provide a voltage (12V or more in your case) in opposite direction, that is the +ve of your charging source to -ve of battery and -ve of your charging source to +ve of battery this creates an electron path in opposite direction for the Battery being charged, this reverses the chemical reaction (this is the difference between Rechargeable batteries and non-rechargeable batteries, the later has no reversible reaction) and takes the chemicals inside to a state when they were charged and produced a potential difference of 12V.

in a way we are reverting the chemicals inside to an earlier state, we are not storing any electrons inside...also based on the drift velocity of the electrons it is fairly impossible for the electrons from the socket to reach your battery before it is fully charged.