Replacing your DSi's battery only requires a Phillips #00 screwdriver and a thin prying tool.
Unscrew the two Phillips screws securing the battery cover to the lower case.
Grasp the battery cover and lift out of the lower case.
Wedge the edge of a spudger in between the top of the battery and its lower case housing and pry upwards to dislodge the battery.
Grasp the battery and remove it from the DSi.