First off, fully dissassemble carb - every piece that was made to come off shoud be off. Most pieces come apart easily enough some require some effort. For stuck choke slide/throttle slides I recomend WD-40 then threading the cable in and pulling really hard on the cable - eventually it will come loose. To get the jet out, there is a brass screw at the bottom of the carb - unscrew that. Look in the hole you just made by taking that out - theres a threaded washer type thingy up in there that a straight screwdriver will take out... do that. Then look up there again thats the diffuser up there, dont try to turn it with a screwdriver it will break, it is not threaded. Instead from the top of the carb push gently down on the tip that sticks into the chamber where the throttle slide used to be. If it doenst give, press harder, if needed us a large diameter blunt metal object like the back end of a large drill bit to press on this tip. Dont use a screwdriver or you may bend it.
Once all these parts are out, soak carb it in carb cleaner overnight - dont just spray with carb cleaner and let sit overnight, get one of those dunk buckets you can get at autoparts stores with the baskets and let is soak in the juices.
Next day pull it out, spray all the little passages with spray carb cleaner just for good measure. Run a thin wire through all the little holes to make they are clear. Then spray it out with some compressed air and reassemble. Take your time, otherwise you will do it again.
search gurtner carb on the wiki for a handy exploded diagram of the carb
I havent had trouble with my gurtner... Its not high performance but it works well. And a new carb would be at least $65 so I am cheap and just keep the old one working.