The simple Italian red sauce is all about variations on a theme. If you have the fundamentals down, you can make almost infinite sauces to fit any context. For an excellent, detailed discussion of the techniques involved, see Marcella Hazan's Essentials of Classic Italian Cooking.
First, we'll look at the simplest variant, which consists of nothing but a yellow onion, garlic, San Marzano tomatoes, extra virgin olive oil, sea salt, and black pepper, and fresh basil (NEVER dried). This simple version illustrates the fundamentals of creating the layered flavour of the Italian red sauce.
SUGO SEMPLICE
Finely mince the onion and garlic with a mezzaluna or chef's knife. Do not crush the garlic using a garlic press or similar, as this will leave an acrid pulp that will not blend as well with the other flavours.
Take a stockpot or saucepan, and lightly but thoroughly coat the bottom with extra virgin olive oil. Add the onion and allow it to sauté at medium heat, stirring frequently, for about 10 minutes. Thorough sautéing of the onion is essential for the flavour blending (insaporire) process. Once the onion begins to become translucent, add the minced garlic, and sauté it for no more than five minutes, stirring frequently to avoid burning.
To the onion-garlic soffritto, add either canned diced San Marzano tomatoes or fresh blanched Roma tomatoes, stirring occasionally. Add sea salt and freshly ground black pepper to taste. After about 30 minutes of simmering, add the hand-shredded basil leaves and toss with your preferred pasta.
VARIANTI
Most variants will involve adding additional ingredients at particular times. However, one variant, known as spaghetti alla carrettiera (Coachman's Spaghetti) maintains the same basic ingredient list, but adds five cloves of minced garlic along with the tomatoes, creating a more subtle garlic flavour.
Possible additions:
Crushed red pepper (to taste, starting when tomatoes are added)
Rosemary (either dried or in sprig form, when tomatoes are added)
Thyme (either dried, or preferrably in sprig form, when tomatoes are added)
Oregano (fresh, minced. A perfectly valid and common addition to pasta sauces. Traditional pizza sauces, on the other hand, do not normally use it. Add when tomatoes are added)
Red wine (chianti, merlot, added, to taste, once the onions and garlic are fully sautéed and thereafter. Adds a full-bodied sweetness)
Traditional Balsamic Vinegar of Modena (hard to find and very expensive, but absolutely delicions in simple sauces. 100 ml bottles are available for USD 60.00 and up, once the onions and garlic are fully sautéed. The better supermarket "balsamic vinegars" (technically: condimento alimentare balsamico) are sometimes good as well)
A rind of parmigiano reggiano cheese (with all the cheese removed, once the tomatoes are added)
Celery (finely chopped, added immediately after garlic is sautéed. Sauté for an additional five minutes)
Tomato paste (makes for a thicker sauce, add in small amounts with the tomatoes)
Tomato purée (also thickens the sauce, but not as much as tomato paste, add at same time)