This is an exciting area of scientific discovery. We know very little at the current time, though more and more scientists are starting to investigate. (There's no reason why you can't one day be one of them!).
Some of the earliest evidence for life-forms come from fossils of ‘biogenic graphite’ (from 3.7 billion year old rocks) and from fossils of ‘microbial mats’ (which are a bit like slimy patches created by lots of algae) from Western Australia. Simple life certainly arose very early in Earth’s history. But from what did these early creatures arise? And from what did their ancestors evolve?
To answer questions like these, scientists look at what makes self-replicating chains of atoms (molecules) form within different conditions, imagining these molecules to be like the first DNA-like structures. Radiation, lightning and simply chemistry (catalysis) seem to be able to produce such replicating molecules, though more evidence may be needed to work out properly if life could really start this way. Either way, once these molecules could replicate, natural selection could get to work, picking out the survivors which would then go onto reproduce and make more, better suited (and eventually better protected) organisms. From this early point of replicating molecules, the chain of evolution would have begun.
Don't forget about PalaeoLab's hands-on evolution workshops for primary schools in the UK, and further resources, including fossil subscriptions and other gift ideas, in the PalaeoLab shop.