I did this a while ago so you can see the battery already replaced but you can get the idea.
Take the precision screwdriver and push it from where the tab is stuck onto the battery near the outside in towards the inside therefore removing the tab from the battery but keeping it attached to the pcb. Repeat on the tab stuck to the bottom of the battery.
Stick on the new battery with the tape making sure to get good contact between the battery with the tabs. If that comes loose then your save gets deleted :-(
Note that the battery goes in upside down (see the polarity markings on the pcb)
Please do not solder the tabs onto the battery as this is very dangerous and could cause the battery to explode