First off, in evolutionary terms, mutation happens exactly once per generation. The time from when you're born until you have offspring is one "tick" of the evolutionary clock. You aren't going to see evolutionary changes in less than the lifespan of the organisms that are evolving.I am trying to understand how you are determinig evolution occured over millions
of years since it appears to be a totaly random process and we were not there to
make any observations. If there is no true limiting factors then what is the difference
of 1 year, 100, or 1 million.
Second, the random process is in the copying and combining of DNA. In simplistic terms, there's some very small but non-zero chance that a particular bit of DNA will be copied wrong. Small changes are quite likely; very large ones are much rarer. It's even less likely that a large change will be beneficial, and that it will be passed down to future generations.
Maybe a conceptual illustration will help: imagine your family has a tradition. On their 20th birthday, the eldest child goes out into a field where a huge bullseye with concentric rings around it is painted - the whole thing is a mile across. There's a marker on the field: the birthday boy or girl stands on the marker and throws a lawn dart straight up in the air. Where it lands is completely random; sometimes it'll be caught by the wind and blow off one direction or another, other times the wind will be completely still and it will fall straight down. In any case, when the dart lands, if it's closer to the centre than the marker was, then the marker is moved to where the dart landed. If the dart lands farther away, the marker doesn't move.
If your great-great-great grandfather started off on the edge of the mile-wide circle, how long do you think it'll take before your family's marker reaches the bullseye?