A few genetic tools exist, but a fairly common method when I was studying it was to use a retro-virus containing failed copy of the gene, and insert it into very young, often single cell embryos, so it would infect all the cells in the target animal, and damage the target gene, either by removing the stretch of DNA it was on, or by changing the portion of the DNA strand which tells the body there is a protein to build here, which I believe is called the promoter.

Nowadays, CRISPR-Cas is one of the easiest tools to use to knock out a gene. You deliver Cas9 (or Cas12a etc) plus sgRNA to cells, which causes a break to be made in a very specific spot. Then the cell tries to repair the break, usually via a messy pathway called NHEJ which often leaves the gene functionally inactive.

If you can live with just partially shutting off the gene, RNA interference is also very popular and can be very quick and easy to do.

Before CRISPR/Cas9, it was actually quite hard to disable a specific gene at will. There are some proteins that can bind to and cut specific DNA sequences, causing function-disrupting mutations, but these are not very accurate and only available for a relatively small subset of sequences.

It's much easier to induce random mutations and then find a gene that got knocked out, resulting in a noticeable phenotypic change in the organism. Random mutations can be introduced with chemical treatments, radiation, particle bombardment (e.g. gold nanoparticles, which can also introduce foreign DNA), or biological systems (e.g. viral vectors in animals, Agrobacterium tumefaciens in plants). Nowadays, many model organisms (e.g. Drosophila, mice, Arabidopsis) have mutant libraries available, which contain specimens (seeds for plants, frozen embryos for animals or at least for mice) which each have a knockout in one gene, and you can order these for your research. A "saturated" library has at least one knockout line available for every single putative gene - putative because some genes are predicted from sequences but have not yet been confirmed to actually be functional genes.