Complex sentence: He won fellowships to the University of Chicago's Booth School of Business, then to the London School of Economics, paying his own way through graduate school with the fellowships and his own earnings and savings.
Split into simpler sentences: He won fellowships, first, to the University of Chicago's Booth School of Business and, then, to the London School of Economics. He paid his own way through graduate school with the fellowships he won and with his own earnings and savings.