I'm quite lucky that throughout the season all of my two stroke tools start and run well but, after being laid up over winter they do sometimes play up until fired up again.
The principle is the same on all of them, tiny carb, a mix of fuel and a spark plug. Unlike most mowers, which have a big enough engine to have a carburettor with a float bowl, two stroke strimmers/saws etc don't have that privilege. All they have is a tiny recess/chamber in the carb moulding with just enough fuel to keep it running. You fill this chamber by priming the carb, the only other thing that keeps the fuel coming after the machine has started is the fuel diaphragm in the carb resonating. If the diaphragm goes stiff/brittle or splits it won't resonate, so the fuel that you have primed in runs out on initial firing. You then keep trying and the plug gets soaked and you end up with arm ache.
If it fires and then dies, the diaphragm could be the reason, or is it not firing at all to start with? You can sometimes, like I did on one the other day, strip the carb, flex the diaphragm in and out gently between your thumb and finger, and then put it back together again. It start first or second pull from cold every time now. A carb rebuild kit is less than a fiver though and takes around ten minutes to swap out. There is a gauze filter on the inlet of the carb as well so worth checking that if you whip it apart.
The photo shows the fuel metering gasket but there are a couple of others, one with the fuel chamber cover and tiny little flaps
, and a general gasket. They are very simplistic carbs to work on.
I would love to sort a drill attachment to start these things when testing but, unlike a mower, the crank is unfortunately the wrong way around to enable this.