How can I set Tasker to change "Network Operator Settings"? I have a "femtocell" in my house due to poor signal quality.
I am living in Japan now. I have to change the Android setting manually each time I get home as described below. There is a auto changer application provided by the carrier, but unfortunately it is not compatible with my smart phone (Xperia Sol 22).

When I get home


Change network mode to "Japan CDMA".
"Airplane mode" On
"Airplane mode" Off


Japan CDMA is under Settings → Other Settings → Mobile Network → Network Mode

When I leave home


Change network mode to "Japan LTE/CDMA".
"Airplane mode" On
"Airplane mode" Off


Japan LTE/CDMA is under Settings → Other Settings → Mobile Network → Network Mode

I have Tasker application in my Smartphone. But I have no idea how to set the tasker program.

Please advice me on this.
I don't believe there is a way tasker alone can do this. 

The fastest way you'll be able to get this done is going to be using a plugin to allow you to recreate your interactions with android. 

The AutoInput is popular choice to do this since the developer is responsive and just took over the Tasker app. Root isn't required for this to work but will most likely have it work more efficiently. Read the instructions provided to you by the app and it will tell you how to record your interactions. 

You'll need to make two recordings, once for enabling these setting and once for disabling the settings. I'm not sure if this will work when your screen is off but having root should improve your chances.