evolution - How did the first sexual animal come to exist?

I am more or less familiar with the evolution theory based on mutations.

Now, starting with a nonsexual being, how did the first organism that reproduces sexually come to exist.

Answer

Big topic yes, but lets hit some high points.

First, sexual reproduction is a no brainer in evolution. In its basis, sex only requires a segment of the chromosome to be heterogamous - that it will not be recombined. In male humans this is both X and Y chromosomes, in other animals it is the female which has heterogamy. Its not the entire chromosome either - the pseudo-autosomal regions of X and Y in humans do recombine.

Sexual reproduction allows some individuals to combine their genomes by donating some but not all chromosomes to offspring. The heterogamous regions are always donated by one parent and the same sex is not allowed to combine with others.

Sexual reproduction is found in plants, single celled eukaryotes as well as animals. The forces that drive the emergence of sex show up frequently enough and are persistent enough for sexual chromosomes to have evolved hundreds of times in plants.

Even in animals, where asexual reproduction is very rare there are multiple configurations of sex determining chromosomes.

Sex goes back to a very ancient trait in eukaryotes related to the haploid / diploid life cycle. In fungi, who are related to the original metazoans, sex shows up when its needed. There the combination of haploid phases may be limited by more than one combination of specific elements. Fungi can have many genders (mating types) - each of may only allow mating to specific types. Others like Saccharomyces allow recombination between any two different mating types.

The earliest single celled eukaryotes related to animals show mating types. The various sexual characteristics related to sexual reproduction, such as placentas, eggs, sperm form and function are all embellishments from sexual selection which vary tremendously from one form of animal to another. The chromosomal functions which became sexual traits are ancient and predate metazoans. They are not necessarily conserved though - they are simple enough to reproduce that they change their characteristics often in evolutionary history.

I should say that all this doesn't apply to bacteria and eubacteria. Why? Because bacteria are much older and have their own systems of gene transfer and recombination with their own rules. They usually have a single copy of their genome (I'd like to hear about exceptions - I think I know of maybe one) which makes quite gender different. The do have something called 'sex' where a pili gene can be found on a plasmid which allows the bacteria to transfer DNA directly, which is like a sex determining locus. But a bacteria may catch gender like a cold - it can not have it, it can get it, it can lose it.

Bacteria are also capable of transferring a single gene or a segment of DNA by various means, including pili, plasmids, phage, and simply taking in the naked DNA that they find laying around.