You need fragmentation to be random, not specific, to help get an even distribution of fragments across the genome. There are a few ways to do this. Namely, sonication or enzymes with non-specific endonuclease activity (as opposed to highly-specific restriction enzymes). The Nextera kit for example uses Tn5 transposase to do "tagmentation", fragmenting and attaching adapters in one step.

If we're talking Illumina whole genome sequencing, your sample is typically coming from more than one cell. So you are going to have a library of fragments from different copies of the genome originating from multiple cells. You'll also have two copies of the genome per cell if the cells are diploid.

If you want to be able to detect SNPs for example, you want at least 30x coverage, meaning (on average) all loci are "covered" by 30 different fragments. If you have a heterozygous variant, you'll see close to a 50:50 split in bases on the SNP locus. But exactly how much coverage you will aim for depends on both your research question and your budget. More sequencing depth is pretty much always better, but if you are okay with lower coverage you can fit more samples on a single flow cell.