You're welcome :) It's a very interesting topic! Unfortunately, I don't know very much about CLL specifically, but the principles are pretty much the same.
Perhaps a good example would be EGFR signalling (because I know more about it ;)). EGF binds to EGFR (Epidermal Growth Factor Receptor), and can trigger a number of different pathways that result in cell proliferation, growth etc. These pathways are implicated in lots of cancers because of this. You can get mutations in EGFR that mean that it's always switched on, or mutations that cause the cell to produce EGF itself (so it keeps EGFR activated by itself), or you can get over-expression of EGFR so the cell receives more "pro-growth signals". All of these things are bad, and will contribute to cancer but are kept in check by certain failsafes. Eg EGFR may be ubiquitylated, which is how the cell marks proteins for degradation. This will keep the pro-growth signals in check. But, there are mutations that can block or impair the ubiquitlyation, or enable it to be bypassed in some way.
I hope this helps. Cancer isn't so much about one root cause, but a combination of different mutations and factors that enable the cell to bypass the failsafes. The cell needs to accumulate different mutations to allow growth, block apoptosis, free itself from its surroundings if it's to metastatise, and perhaps recruit blood vessels to provide itself with oxygen. It's a very complex process with lots of different mutations that can contribute to tumourigenesis.