If using the standard method, add water to a 3-quart saucier or saucepan and set over high heat. Sprinkle in cornmeal while whisking (water does not have to be boiling).
Bring to a boil, stirring frequently. Let boil, stirring frequently, until polenta thickens enough that it starts to spit. Lower heat immediately to prevent spitting and continue to cook, stirring frequently with a spoon or silicone spatula and scraping bottom to prevent scorching, until polenta becomes thick and pulls away from side of saucepan, about 30 minutes for pre-soaked cornmeal and 50 minutes for dry cornmeal. Season with salt.
Stir in butter or olive oil using either a spoon, silicon spatula, or whisk. If polenta forms lumps, beat vigorously with a stiff whisk to remove. If polenta becomes too firm or begins to set, add a small amount of water, stock, or milk, and beat in with a whisk until fully incorporate and no lumps remain.
Serve right away with accompaniment of your choice, or scrape into a vessel and chill until set, then cut into pieces for grilling, searing, or frying.