Oh jeez... It's such a complex topic that asking for a basic answer is asking a lot, imo, and I'm nowhere near educated on the topic enough myself to give a very good answer. I was raised with creation science in a religious school setting, so I'd probably know more about that than evolution. Given all that, I'll try and give as basic an answer as I can muster
The science behind evolution is similar to forensic science, and just like forensic science, is bolstered by many other fields of science that work in tandem to help paint a clearer picture of past life and it's history. Those other fielda of science include ones such as geology, astronomy, paleoclimateology, paleontology, etc etc. The evidence gathered by all of these different schools of science seem to show that, over a nearly unfathomable period of time, life seems to have slowly mutated over that time given the fossil record so consistently and predictably occurs in tandem with other events and occurances uncovered in these various other fields of science - especially paleontology and geology
Just like all other theories, evolution has to stand up to the scrutiny of the scientific community as a whole. There's a lot of incentive for those in the scientific community to bring down a theory as sound and established as evolution is, but none have been able to do so yet - it is the very best theory we have that shows what the history of life on earth looked like, and all the evidence found and continue to find only serves to strengthen it. There's really nothing to suggest that will change any time soon, either
If anyone would like to correct me or add anything else, please do!