How can I add ~/.local/bin to my PATH?

If you make a ~/bin folder in your home folder, it'll already be in your default path. No need to modify anything, or add folders to a hidden .local folder. Create the ~/bin folder, log out, log back in, and open a terminal window, and you can confirm the path by typing echo $PATH.

Update #1:

If you decide to use ~/.local/bin anyway, add this to the end of your ~/.profile...

# set PATH so it includes user's private ~/.local/bin if it exists
if [ -d "$HOME/.local/bin" ] ; then
    PATH="$HOME/.local/bin:$PATH"
fi

Then log out, log back in, and your new path will be available.

The PATH variable gets changed when this shell command is executed:

export PATH=$PATH:/your/new/path

The ~/.bashrc and ~/.profile will be executed automatically when you open a bash session (normally when you open a new terminal window/tab).

So if you want to change the PATH in current shell session only, you could just type export PATH=xxx and execute it once. But if you want to make it difference permanently, you should add the command above into ~/.bashrc or ~/.profile.