A typical straight vinaigrette has oil, vinegar, usually mustard (for a little flavor and for its emulsifying properties; I suggest Dijon), a little minced shallot (optional), salt, pepper and, sometimes, a pinch of sugar. Other things like fresh or dried herbs, spices, etc., are often included.
The first thing to establish is the proportions you like. Note that these can vary a bit, depending on the vinegar you use, the oil, etc., but I like roughly 1:2 in most cases. So:
Start with your dry stuff and the mustard in the bowl first - let's go with a teaspoon-and-a-half of Dijon, a couple turns of the peppermill, a couple or three pinches of salt, a tablespoon of minced fresh shallot if you've got it (or minced sweet onion) - but don't worry about it if you don't as we're just establishing a baseline here, and a pinch or two of sugar, if desired. Mix to combine with a fork.
Add 1/4 cup vinegar of choice. For basic vinaigrettes I use red or white balsamic, or good white wine or champagne vinegar. Whisk well with the fork then add a few drops of your oil of choice (I mostly use a good evoo for basic vins - my preference is Morea), whisking with your fork constantly, then continue to add the oil in a very slow steady stream, till well combined and emulsified. Use 1/2 cup. Taste. Adjust salt. That's a 1:2 vinaigrette. If that works for you, good. If you want it less vinegary you can either add more oil or, if you prefer, you can add water, adjusting the salt and other seasonings as needed. You can add a pinch more of sugar but, contrary to popular belief, sugar can only go so far in balancing tartness. It doesn't do much for acidity balancing. If too acidic it's better to up the oil, add water, or do a bit of both.
[Note: if you have a handblender (AKA immersion or stick blender) you can make vinaigrettes and other dressings very quickly using that. You can also use a regular blender but, depending on its size, you might need to double quantities so that the blender can actually do its job.]
Once you have a base established you are good to go with literally countless variations. When used to your base quantities you can simply eyeball amounts. Adjustments are a breeze to make on the fly.
Basic additions and substitutions:
Add minced fresh or dried herbs (or a combination of both) to the mustard at the outset. Want a 'basil vinaigrette': add a tablespoon of minced fresh basil. A good herb vinaigrette might be, say, a couple or three teaspoons of minced fresh parsley, a t or two of basil, a little fresh or dried thyme, some fresh oregano or marjoram. For 1/4 cup of vinegar figure on 1-2 tablespoons total on the herbs.
You can up the Dijon to make it more of a mustard-y flavor finish. You can use a good honey Dijon - or simply add some honey to the regular Dijon you have when you mix it in the bowl.
You can switch sweeteners: agave nectar, honey, date molasses, maple syrup (try that with a salad that includes apple and cheddar cheese), are just a few examples.
You can switch vinegars or use a blend of two or more. I'm fond of cognac vinegar for beef salads (grilled steak, e.g., sliced and served atop tossed greens), fig vinegar, unfiltered organic apple cider vinegar, orange muscat vinegar, et al.
You can sub some fruit juice for all or part of the vinegar. (If the juice is tart you can go with it as is; if sweet, cut its sweetness with some vinegar.) Cherry juice and red or white balsamic 1:2; apple juice and cider vin 1:2 or 1:1; straight ruby red grapefruit juice or other tart citrus juice; the list goes on. One of my very favorite vinaigrettes for summer is lemonade vinaigrette. Replace the vinegar in your base with a good lemonade. With minced fresh basil and/or other herbs, Dijon, a touch of honey, plenty of pepper, it makes a great dressing for a summer salad - and is nice drizzled on grilled chicken, grilled corn-on-the-cob, etc. Ruby red grapefruit vinaigrette is a favorite for grilled-then-chilled shrimp that are served on top of a tomato-fruit salsa (finely diced tomato, sweet onion, finely diced ripe strawberry, minced jalapeño, finely diced pineapple and/or watermelon), the whole shebang drizzled with the grapefruit vinaigrette.
You can use different oils: walnut and almond oil are favorites, as are avocado oil hazelnut oil and others. They are best when wanting to add or boost nut flavors (such as when you are adding toasted nuts to a salad) and also work well with grilled meats and salads that contain dried berries.
More on this later, and I'll get into creamy dressings as well. They are simple too.