Purée tomatoes using an immersion blender, or by mashing them up by hand.
Heat the olive oil in a medium sized pot over medium heat. Add the onions, and cook until they are translucent (about 5 minutes). Do not get any browning on the onions. Be sure that the oil maintains a constant simmer.
Add the garlic, and continue to cook over medium heat for another 2-3 minutes. This process infuses the oil with the flavor of the onion and garlic.
Now add your pureed tomatoes, basil and ½ tsp salt to the pot, mixing to incorporate. Simmer for 15-20 minutes.
Taste, and add another ½ tsp salt, or more to taste.
Use this sauce to simmer homemade meatballs in (you can find my recipe here), or as pasta sauce.