Typically the method goes something like this.
Power computer down. You can optionally unplug any cables attached to make the process easier.
Close the lid.
Flip the computer over.
There should be one or two lock slots that hold the battery in the case. Slide them to the unlock position.
Disengage the battery from the case.
Flip the case back over.
Reattach any cables you took loose.
Open your lid.
With battery in hand, go to online battery store of choice.
Enter model number.
Reenabling it in the system is the same as above, in reverse.