There are many ways life on earth could have begun, but we can't really say because the traces have pretty much been wiped out by subsequent biological and geological events.

It's not hard to envision a reducing atmosphere (no free oxygen around to destroy complex chemicals) with several energy sources and an ocean.  We know that such an environment would, within weeks, produce a soup of amino acids and similar chemicals.  Then give it a few million to a few hundred million years.  All you need is one molecule that makes a copy of itself from this soup -- not even an exact copy, just one that perpetuates, and then natural selection happens automatically to build the complex machinery people wonder at now.

Life was of a single-celled nature after that for a couple billion years, no doubt refining the processes, before striking out into organisms we recognize as getting advanced.