How to install software into the home partition?

I have read some article about home partition in Ubuntu but I don't know why it is used widely. Because software I have installed via Ubuntu software center or deb package, they all automatically install into root partition like /opt, /usr or something like that. Anybody can give me some suggestions?

User's home folder is for user's documents, all installed software in a typical Linux distribution goes into /usr and is available to all users.

If you need to install some program into user's home folder (say, to make it available to that user only), the most straight-forward thing would be to download a source tarball and compile it with a custom prefix:

./configure --prefix=/home/jack/myprogram
make
make install

of course, the actual commands to compile will depend on the software you're installing.

However, I have a feeling your desire to install programs in your home folder is guided by some misunderstanding. This is by no means a recommended or normal way to install software.