Read pages 49-58 of Chapter II of [Silverman-Tate]. For a much more clever (and more terse!) account of the same theorem, you might also want to look at Cassels, Sections 9-12, which I will hand out to you (reading Cassels is optional). Also, try out MAGMA, PARI, and MWRANK using the commands magma, gp, and mwrank on meccah, respectively, and browse some of the big documentation handout.