A solar garden light has a small solar panel fitted onto the lid which charges one or two AA batteries during the day when the sun is out. At night, a low-power light emitting diode or LED operates from the stored charge. The lamp is ready to use right out of the box with minimal assembly and needs no wiring. You do have to ensure the battery is connected, however, and you may have to turn the light on. One day of full sun should get the LED shining at night.
Look for any light sources near the garden light before you disassemble it. Illumination from a porch light or street light can be enough to trigger the light dependent resistor, or LDR, and prevent current flow from the batteries to the light. The purpose of the LDR is to keep the LED off during the day while the batteries are charging. It deactivates when the sun goes down, allowing the LED to operate, but will remain active if light is hitting the panel from another source.
Unscrew the cover of the fixture and turn it over. There may a small toggle switch next to the battery compartment. It must be in the "on" position for the light to operate.
Look for a small piece of clear plastic protruding from the battery compartment and pull it out if you see one. The manufacturer installed it to keep the batteries fresh, and you have to remove it before the light will operate.
Remove the batteries and charge them in a battery charger, then reinstall them. Cover the solar panel with your hand to deactivate the LDR and check if the light illuminates. If it does, the panel may not be receiving enough sunlight during the day to charge them. Relocate the fixture to a sunnier location or clean the panel with soap and water. It's also possible that the batteries have gone bad.
Unscrew the battery cover with a #1 Phillips screwdriver and inspect the wiring if the light stays off after you charge the batteries. If you find a loose wire, resolder it to the terminal with silver solder and a soldering iron. You can tell from which terminal a wire has separated in two ways. The terminal usually has a coating of solder and the wire will reach that terminal and no other. However, don't do this if you are not familiar with how to use solder -- you risk getting the melted solder on your skin.