Tecumseh Carbs are fairly simple units. The float model carbs are easy to rebuild/repair.. Before you start, one thing you will need is a repair manual. (I have free pdf's for members).
There are some common problems with carbs that should be checked before you start a rebuild. Many times the following items will correct the trouble your engine is having. You will still need a repair kit to replace certain gaskets and seals that should be replaced whenever disturbed.
One of the more common problems is the flooding of the carb. If this is your complaint check the float first. Remove the float bowl, float pin and remove the float. Be careful that you do not loosen the float needle valve. Now shake the float and listen for gas inside. If the float sloshes, replace it with a new one. Replace the float needle valve seat and adjust the float per the factory manual. Replace the float bowl gaskets.
If you are experiencing performance problems and suspect the carb, you will have to remove it from the engine to correct the problem. After the carb is off the engine there is one thing you need to check before going any further. Remove the float as above. Now hold the choke and throttle butterflies so that you can shake the carb without them making a sound. Shake the carb and listen for it to rattle. If you do not hear the rattle, the emolltion tube is stuck. This tube is sealed into the body of the carb during manufacturing and can not be replaced. The carb will need to be replaced. Also if the aluminum body of the carb is corroded inside, any rebuild will only be a temporary fix. Once the corrision has started it can not be stopped.
If everything checks out up to here, a rebuild and cleaning should fix the carb. However there is one more tricky thing you will need to do. You must remove the welch plug on the side of the carb. This can be done by driving a sharpened small punch or screw driver through the plug and popping it out. Take extreme care when doing this procedure. There are two jets cast into the carb body under this welch plug. If you damage them the carb will have to be replaced. With the welch plug removed and the main jet (in the bown nut) out the three holes that need to be cleaned are exposed. Using a piece of soft tag wire clean these holes. Now cdlean the complete carb with carb cleaner.
Re-assemble the carb. Make sure that the needle valve seat is completly down into its bore. After driving in the new welch plug, paint it with finger nail polish to seal it. Adjust the float height using a #4 twist drill as directed in the repair manual