Although this may be a simple solution, you may overlook whether you have turned the switch on. This does not apply to all trimmers, because some do not have switches.
Check the spark plug on the trimmer to see if it is wet on the tip. If so, the plug may need to be replaced. When replacing it, ensure that you gap it at .025 to avoid the same issue in the future.
Consider what type of fuel you are using. Ensure that your fuel mixture is fresh and has not been sitting for months at a time, especially over the winter. Use a fuel stabilizer for maximum efficiency.
If you attempt to start your line trimmer unsuccessfully too many times in a row, the engine may be flooded. You will smell fuel if this happens. Allow your weed eater to set for at least 15 minutes to give the fuel time to vaporize before trying again.