Use the battery's plastic pull tab to lift and remove the battery from the upper case.

If you're installing a new battery, you should calibrate it after installation:

Charge it to 100%, and then keep charging it for at least 2 more hours. Next, unplug and use it normally to drain the battery. When you see the low battery warning, save your work, and keep your laptop on until it goes to sleep due to low battery. Wait at least 5 hours, then charge your laptop uninterrupted to 100%.

If you notice any unusual behavior or problems after installing your new battery, you may need to reset your MacBook's SMC.