I started by CPU-mining on my VPS. Without really knowing what I was doing, I managed to solve a block and score BTC50.
BTC50 using VPS?? That's cool!

How long did it take to generate one block?
Probably several months, at least...think it happened in May 2011. It's most likely not feasible today, as you won't see much more than 10-15 MH/s from it, depending on what your VPS uses (mine have given me 4-8 Xeon or Opteron cores). The only point in its favor now is that if you already have a VPS for other purposes, mining on it won't cost you anything extra.