This is simple. Just create a new user with its home directory set to the one you need him to have access to (this command must be run under sudo or in root shell):
adduser --home /restricted/directory restricted_user
This will create a user restricted_user, the directory /restricted/directory and then permissions on the directory will be set so the user can write to it. It won't have an ability to write to any other directory by default.
If you have the directory already, you can run adduser command with a --no-create-home option appended and set permissions manually (also with root privileges), like: