We know that two things cannot occupy the same space at the same time. Although spiritual substance need not be subject to the law of physics, we might still ask, "Where does this additional neshamah fit? Was there previously a vacuum in the space it now occupies?"
As the Sabbath approaches, we create a place for the additional neshamah by discarding much of the weekday matter we have accumulated. To the extent that we rid ourselves of the weekday problems, to that extent we can receive the additional neshamah of the Sabbath.
We are instructed to approach the Sabbath with an attitude that all our weekday work has been totally completed, and so nothing has been left undone that could cause us to think about it on the Sabbath. Weekday activities relate to the means of living, while the Sabbath represents the goal of life. It is the time when, freed from all other activities, we can direct attention to the study of Torah, to prayer, and to contemplating on what God wants of us. Vacating the thoughts, stresses and worries of weekday life leaves "space" for that extra neshamah.
We can begin preparing to receive the additional neshamah during the week: we can consider our weekday activities as merely the means to earn a livelihood, and then look forward to the Sabbath, on which we will be able to focus on the purpose of life.