I feel like stepping in a bit, before Hambone gets all "If men did in fact evolve from apes, why are there still apes?" on us. I'm having a "Woah, I slept through this class but actually recall stuff" moment.
In divergent evolution, a species is reproductively isolated from part of that species, and due to different environmental pressures, individuals in the species better adapted to the new environment will evolve. For example (entirely hypothetical), say there is a species a bit like the modern giraffe, but with a much shorter neck. A natural disaster occurs, causing a herd of this species to separate. In one environment, the food is on the floor, and these "giraffes" need to strain their necks to reach. In another, the food is high in the trees, so the "giraffes" with the longer necks will be able to reach it. The "girraffes" unable to reach food will die. Over time, mutations occur (I'm assuming you understand basic 6th grade cell theory ), and the "giraffes" able to reach the food in their respective environments will thrive and reproduce, creating more "giraffes" like themselves. Many generation later, in population 1 you have short legged "giraffes" with bendable knees able to easily eat food on the floor while in population 2 you have your standard tall, long necked giraffe. Somewhere else, you probably still have the original creature, chillin' in the environment it was before the environment pressure that separated them.
Convergent evolution is the opposite (two different species come together and become more similar because of they live in an same environment). An example of this would be the long tongue evolved by butterflies, some moths, and hummingbirds to suck the nectar from flowers. Different animals need to accomplish the same task, and therefore evolved analogous structures - that is, structures that are similar to each other in function, but different in structure. This would suggest that the animals do not share a common ancestor. Very different from homologous structures, such the human arm, whale flipper, and bat wing. Like.. in this picture:
The similarities suggest a common ancestor. However, convergent evolution has made these "arms" adapt and suit the environments for which they are necessary.
So, lol, I think you can see how easily we could have evolved from apes?
Now, you're saying "But Izzy, where did the first cell come from?"
Well, the dude that did the experiment with the steak and the flies (Redi? Maybe?), Louis Pasteur, and some other dude disproved spontaneous generation. However, the state of the Earth was much different a few million/billion years ago. Pretty much what happened (be happy, I'm summing up a super boring two hour long film for you): An asteroid containing Carbon, Nitrogen, Oxygen, and..something else hit the earth, and the impact caused them to bind together, forming amino acids, the basic building blocks for life. This was eventually proven in a lab by taking a chunk of asteroid and smashing it in an enormous collider. From here, you get simple simple simple prokaryotes, feeding off of the environment, getting bigger, competing, and growing. Certain ones feed off of different things, others on other, and they're different. Eventually, a bigger prokaryote consumes a smaller prokaryotes, this smaller prokaryote being mitochondria in animal cells and chlrorplasts in animal cells. ..And... tada, embiosymbiosis, and we have our first cell! The rest is self explanatory, really. ..If you believe in evolution. Which you don't. Making this a waste of time. However, it's scientifically sound, while nothing you say is, so I'm happy.
Why couldn't I remember this crap on my exam? ...Umm. Sorry if that doesn't sound.. super sound. Trying to remember things from freshmen bio. >_>