How does crossing over and independent assortment insure genetic variability?

It doesn't always. When crossing over occurs sections of nucleotide bases are switched. Lets take for example you have an original DNA of TTCTCCGATAGT and crossing over occurs to change this into TTCATGGATTCT. When this is now read by the mRNA only ATG will become a different protein meanwhile AGT on the original will be made into the same protein. This is because you have to look at the codon table to see which codons become which protein. Different codons may produce the same proteins so crossing over does not always ensure genetic variation but is gives genetic variation a more likely probability of happening. As for independent assortment, this doesn't lead to genetic variation. Really independent assortment will just lead to different phenotypes being expressed.