In laymans terms how do you arrive at measurements that show the movement of the solar system and galaxies .?

I have accessed the web page : http://arxiv.org/abs/astro-ph/9601151 posted by C.H.Lineweaver,L.Tenorio,G.F.Smoot, P.Keegstra, A.J.Banday and P. Lubin , submitted 26 Jan1996 and revised 4 Sept 1996 . This (to my understanding) relates to the subject of yzing data from the COBE Differential Microwave Radiometers to arrive at the conclusion our Solar system is moving at [about] 300 kilometres per second in the direction of the constellation Leo . This paper is written for and in the language of the mathematicians and physicists who specialise in such subjects , neither of which I am .