Hello, I have a craftsman gas hedge trimmer that will not start. What are some things I could checl out to try to get it working

Two items fairly easy to check; the condition of the spark plug and whether the ignition coil is healthy. The plug must be removed to check it for fouling (a buildup of deposits near the spark gap) and also wipe the insulator of the plug clean and inspect it carefully for fine lines; a cracked insulator (not uncommon) will provide a path for the spark voltage to ground before it reaches the spark gap. The ignition coil can be checked by sight in a shady area (sunlight makes it tough to see). Pull the plug wire free of the plug and insert anything metallic into the female connector that will extend the contact. Position your extension near some metal part of the engine and watch this gap as you tug on the starter rope. You should be able to see the spark appear a couple of times with each pull of the rope to its limit.
These coils are not very well made and cost $30-40 US to replace.
Once you have access to the coil. use some gauge (could be a knife or screw driver blade) so you can re-gap the coil if a new one is installed.
I suggest that you go to the Sears website below and enter your model number. You should find it listed there and it will have a parts breakdown of your trimmer along with part numbers, etc.:

Sears parts dept.

Using this you can orient yourself on the innards of the trimmer.