The question is a broad one. Is this a cooking question or is it a question of scientific process? The first person answered the scientific principle aspect, so I will offer a cooking answer.
A basic vinaigrette is generally one part acid (vinegar or citrus juice) to 3 or 4 part oil. From that base, many variations can be made. An important thing to remember is that there are many options as to what the acid could be as well as the oils. Acids could be lemon juice, lime juice, grapefruit juice or orange juice. Juices are best when fresh squeezed. As for the oils, you may choose a neutral tasting canola, safflower, sunflower or grapeseed. You could also choose a more flavorful oil such as extra virgin olive oil or any of the nut or seed oils.
If you choose a neutral oil, you may need to add a touch of mustard to help the oil and acid bind better to make a more stable emulsion. (An emulsion is a colloidal suspension of a liquid in another liquid.) Neutral-tasting oils need less acid or vinegar.
If you choose a more flavorful oil, more acid is needed to balance out the taste.
I hope this has encouraged you to experiment in your kitchen. Remember the closer to nature substances are, the healthier they generally are. If you avoid store bought dressing, you are not taking in all the overly processed ingredients or the preservatives. Homemade is a healthier (generally speaking) and often less expensive alternative.
I am wondering of you are talking specifically about mayonnaise? Mayonnaise is a nice example of a science concept in an everyday use. It is made from egg yolks, oil, and vinegar, and the trick is to get the oil and the vinegar to stay mixed, and not separate.
The egg yolk works as an emulsifier. An emulsifier is a chemical that prevents separation. It is made of molecules with two distinctly different ends; one end is compatible with water (hydrophilic) and the other is not (hydrophobic). The emulsifier is beaten in with the fat, and the mixing breaks the fat molecules apart and allows the emulsifier molecules to attach to them. Then the vinegar is added slowly, and the water-loving ends of the emulsifier attach to it, creating a stable structure that will not separate. The key to making it successfully is to beat the yolks and oil very thoroughly, which assures that every oil molecule gets attached to, and then add the vinegar slowly for the same reason.
A number of other recipes for sauces -Hollandaise, for example- rely on the same scientific principle.