Removing the Carburetor Float (updated 8-4-2017)
This is for informational purposes only. Proceed at your own risk.
Here's one of the things that the manual tells you to do, but does not tell you how to do it.
There is a potential for serious damage to your carb body if you are not careful.
These are the parts you are trying to get to by removing the float.

When you remove the carburetor float, float needle valve, and seat you can:
Examine the parts for wear (tip of needle valve and o-ring).
Clean residual gum or varnish left behind by evaporated gasoline.

A friend of mine repairs small engines. I have seen him take a small hammer and punch, and tap a float pin out in the blink of an eye.
If you are tempted to do this, please be careful, and put a support under the post you are tapping on (and don't blink!).
The aluminum posts are fragile. A heavy blow will break them off.
If you are still determined to remove the float, I would like to offer an alternative method of removing the float pin.
Using a pair of adjustable pliers (channel locks), gradually increase the pressure on the pin, and push the float pin flush to the post.

Then use a small brad or finishing nail to complete pushing the float pin through the post.

I feel that by using the pliers, I have more control over how much force, or pressure, is placed against the pin and post.
There is still a possibility of damage by heavy handed use of the pliers.
Here's the carb with the float removed.

Remove the retaining screw and seat, and clean the parts.
(If the seat is stuck in place, you may need pliers to remove it. The brass seat is easily damaged by steel tools. You may need to replace the seat with a new one if you damage it.)

Examine the o-ring. Replace it if it is dry and flattened. An old o-ring is one of the causes for the carburetor to leak gas.

After cleaning the needle valve and seat assembly, put everything back in the carb body, and press the float pin back in place.

Before you put the carb bowl in place, check to see that the float is working properly.
Gently press down on the float, and release it.
It should move smoothly and spring back into place.
If you keep your TW for a long time, you may be performing this procedure more than once.
To make it easier, you can drill the hole in the float post slightly larger, so the pin easily slides in and out.
It won't fall out. The shape of the float bowl will keep it in place.

jb
This is for informational purposes only. Proceed at your own risk.
Here's one of the things that the manual tells you to do, but does not tell you how to do it.
There is a potential for serious damage to your carb body if you are not careful.
These are the parts you are trying to get to by removing the float.

When you remove the carburetor float, float needle valve, and seat you can:
Examine the parts for wear (tip of needle valve and o-ring).
Clean residual gum or varnish left behind by evaporated gasoline.

A friend of mine repairs small engines. I have seen him take a small hammer and punch, and tap a float pin out in the blink of an eye.
If you are tempted to do this, please be careful, and put a support under the post you are tapping on (and don't blink!).
The aluminum posts are fragile. A heavy blow will break them off.
If you are still determined to remove the float, I would like to offer an alternative method of removing the float pin.
Using a pair of adjustable pliers (channel locks), gradually increase the pressure on the pin, and push the float pin flush to the post.

Then use a small brad or finishing nail to complete pushing the float pin through the post.

I feel that by using the pliers, I have more control over how much force, or pressure, is placed against the pin and post.
There is still a possibility of damage by heavy handed use of the pliers.
Here's the carb with the float removed.

Remove the retaining screw and seat, and clean the parts.
(If the seat is stuck in place, you may need pliers to remove it. The brass seat is easily damaged by steel tools. You may need to replace the seat with a new one if you damage it.)

Examine the o-ring. Replace it if it is dry and flattened. An old o-ring is one of the causes for the carburetor to leak gas.

After cleaning the needle valve and seat assembly, put everything back in the carb body, and press the float pin back in place.

Before you put the carb bowl in place, check to see that the float is working properly.
Gently press down on the float, and release it.
It should move smoothly and spring back into place.
If you keep your TW for a long time, you may be performing this procedure more than once.
To make it easier, you can drill the hole in the float post slightly larger, so the pin easily slides in and out.
It won't fall out. The shape of the float bowl will keep it in place.

jb