Hopefully all the dirt's been caught by the mesh screen in the carby.
First, I would suggest back flushing the intake line and the big filter on the line with something pressurised - $1 degreaser is good
Then take the carby off (mind the breather hose on the filter housing) and undo the four screws on the bottom of the carb (I suggest work on a piece of white paper so nothing gets lost in rags or rolls off without noticing).
Removing the black plastic portion of the carby, you will see the metering diaphragm - if its pliable, all should be well.
Now remove the next metal portion (which will have the barbed main inlet fuel line connection on one side). Mind the conical spring on the fuel pump diaphragm. Look on the other side of the metal mid body and you will see the mesh gauze screen. Poke a small piece of welding rod or thick wire up the fuel line connection to pop the mesh out. Squirt through the mesh with degreaser and check there isn't any dirt under where the gauze sits.
Reassemble slowly and carefully and you should be good (you could film yourself disassembling if you are worried of losing anything
Unfortunately, thats the best I can describe it - just be methodical and you will be fine.
