Wikipedia is your friend (see the article below and its references).
In brief: Uracil is removed from the DNA by (at least) two mechanisms (UNG or MSH2/MSH6 dependent), which ultimately leads in the excision of a short strech of the U-containing strand. The resulting gap is filled up by patch polymerases that have a high error rate and will therefore cause mutations other than the initial C-to-U transition.
BCR-dependent activation of the cell is a requirement for the induction of SHM, however it is not sufficient. AID activation is potentially detrimental and therefore tightly regulated, and I am not sure whether the downstream signaling cascade leading to AID activation is currently fully understood. SHM usually only occurs in the germinal center and requires additional signaling from T cells. CSR is not strictly T dependent, but T cell signaling nevertheless has a strong positive effect on switching. Finally, since AID only acts on ssDNA, the target loci have to be transcriptionally active, which is another layer of regulation.
CD40L (CD154) and cytokines from T cells induce signaling cascades that turn on programs typically only active in germinal center, esp expression of AID. double strand DNA breaks occur and during that repair, error prone polymerases introduce errors.