Determine what kind of output you want your lamp to provide and how much power your lamp will require with ordinary use. For example, a typical 60 watt incandescent bulb used for two hours a day would require a solar panel capable of generating at least 120 watt-hours on most days of the year. Such a panel would cost hundreds of dollars at retail. Consider a fluorescent or an LED instead, as these kinds of lighting require only a fraction of the power. See Resources for website that will help you determine your power needs.
These are not practical to build on your own. Shop around until you find the product you like and a seller you trust. This is the major expense of your solar lamp project, but a quality solar panel will generate free electricity for many years.
The solar panel itself will produce DC power. If you plan to use fluorescent or LED lighting, you will have to buy lights that are specifically designed to use DC power or you will have to buy a power inverter to convert the DC power into AC. Note that some smaller inverters may not be able to correctly power fluorescent bulbs, so ask about this if you plan on using fluorescent light. Be sure to ask about how much power they will waste in the conversion process, and figure it into your gross solar power generation needs.
Your solar energy will be collected during the bright hours, but your lamp will run when it's dark. Between these times, the energy will have to be stored in a battery. Get a battery rated for a high number of recharges so that you won't have to replace it often. Here too there will be some power waste, so find out how much and multiply your gross power needs accordingly.
The panel will probably have to be installed outside, facing south, with good exposure to sunlight. The roof is usually the best place. Installation should be easy enough to do by yourself. You may also be able to install it indoors if your lamp's power needs will be very low. Check with the solar panel seller to learn about possible indoor use.
These should both be located securely and protected from the elements. If there is an inverter, the battery will come first.
In addition to connecting the panel to the battery, you will have to separately connect your battery to the inverter and to the lamp. All wiring should be run in a protective conduit, and outdoor portions should be resistant to the elements. Locate your lamp near the solar panel to minimize voltage loss along the wire. Don't forget to ground your circuitry.
This step is not necessary if you will be purchasing a new lamp or reusing an existing one. But if you're going to build your own, you will need to design and construct the lamp and wire it accordingly. The key materials for doing so are readily available at the hardware store.