Electrolytic Capacitors such as these are polarized, meaning they have a positive lead and a negative lead. Pay close attention to which leg is where on the old capacitor and be sure to correctly orient the new one

Clean up the space where the old capacitor was glued down and tin the pads with fresh solder. Be sure to clean up any leaked substances and corrosion with 99% Isopropyl Alcohol.

Bend and clip the leads to a manageable length on your new capacitor and solder it in place. Be sure that when you lay the capacitor down it doesn't extend over any gold circles on the circuit board as these are places that the upper case makes contact with when the Game Gear is assembled