The beauty of biotechnology is that the same techniques can be used whether you are studying humans, mice, fruit flies, or the ugly naked mole rat.
A naked mole rat. Image from here.
A human gene can even be cloned into a plasmid and expressed in insects and bacteria.
The same DNA sequencing techniques have been used to sequence the genomes of organisms, from humans to yeast. PCR can be used to amplify DNA from any organism whose sequence is known.
We can perform a Western blot to look for a protein from any organism. Well, as long as we have an antibody for that protein. We can do DNA microarray analysis on several different organisms, too. Gene chips have been created for many different organisms.
Why can these techniques be used for any organism? We'll take universality of the genetic code for $200, Alex. As different as organisms are (compare a human being with a fruit fly), our DNA contains the same four building blocks or bases: A,G,C, and T. Base pairing rules are even the same across species.
The techniques used to extract the DNA from different organisms may differ slightly, however. After all, organisms show structural variations. For example, the technique for bursting open the cells has to be a little different depending on if the cell is surrounded by a membrane (animal cells) or a tough wall (plant cells). The structural variation is part of the diversity created by the four bases.
Wait! What? We know we told you the four bases unite all organisms. They are also responsible for making organisms different. The sequence of the four bases is what creates diversity among organisms.
The four bases are both the yin and the yang. The unity and the diversity.