Use a Spark tester (which can be found at any automotive supply store), to test the spark.

To use it:
- Remove the boot from the spark plug on the trimmer.
- Plug the end of the tester with the metal probe into the boot.
- Connect the other end of the tester to the spark plug.
- Give the trimmer a couple pulls, while watching the testers spark chamber.
No Spark
If you don't have a spark, you probably have to replace the ignition coil/module. There's a good YouTube video that shows how to replace a lawn trimmer ignition coil. Your model may vary, but the procedure will be similar.
Weak Spark
If you have a weak spark, try cleaning, regapping, or replacing the spark plug.
How a trimmer ignition system works
The ignition system is made up of 3 major parts. A magnet (located on the flywheel), an ignition coil, and a spark plug. When you turn the engine (pull the cord), the flywheel rotates. When the magnet on the flywheel spins past the ignition coil, a current is induced. This current travels through the ignition wire to the spark plug. The electrons want so badly to return home (ground), they jump the gap in the spark plug. As they jump, they produce an electric arc (also known as a spark). This arc ignites the fuel air mixture in the chamber, and the trimmer starts.