Note: Carburettor types vary from different model engines, this is a general guide so you get the idea of the process. Hope it helps.
Once you have removed all of the connecting hoses and rods from the carby locate the 2 bolts that go through the airbox and into the carby, there's one on each side of the air box.
Remove the long bolts, remove the airbox, then remove the carby.
Once the carb is removed locate the 4 philips head screws that hold the fuel bowl to the carby. These screws often get quite burred from silly people using the wrong size philips head screw drivers over the years! Note: If the screws are in bad shape you can use vice grips to get them undone.
Remove the bowl with care not to damage the O-ring gasket, have a rag handy, there's usually fuel in the bowl and it will spill out when you separate the bowl from the carb.
With the bowl now removed undo the 3 screws circled below. The 2 brass ones are plugs that cover your jets, the big one covers your main jet, the smaller one covers your pilot jet.
Remove the silver float pin screw, then remove the float and pin. Be careful, the pin will fall out, don't lose it.
Next step is to remove the pilot jet, you will need a small flat blade screw driver to remove the jet. Make sure it's the right size, the jets are soft and you don't want to damage them.
This is what the pilot jet looks like, in a lot of cases this is the source of the problem. The little holes get clogged effecting the performance of the motor.
You can remove the main jet but I usually leave it in, there's only one hole in it and it cleans up OK with a straight blow through it with the carby cleaner.
Next step carefully remove the diaphragm cover, be careful here and make sure you don't damage the diaphragm. It sits between the cover and the carb body.
Thats the end of the dis-assembly.
Now clean the carb thoroughly with the carby cleaner, spray it in all orifices and over all parts, spray the float, spray the pilot jet, spray the main jet, spray everything until it's squeeky clean!
Spend a little time on the bowl.... This is where residue sits and sometimes bonds to the surface of the bowl. You may need to agitate this area with a small cleaning brush (old tooth brush works well) or rag, spray, agitate, spray, agitate, spray agitate... until squeeky clean.
So... you have thoroughly cleaned all parts and removed any surface residue, blown out the jets and made sure they are all clear with no blockages. Now re-assemble the carby and re-install on the motor.
You may need to adjust the position of your throttle or adjust your idle screw (the screw with the spring circled below).