Rice pudding is mostly patience running on top of a ratio: about one part rice to four parts milk, held at a bare simmer for the better part of an hour, stirred often enough that nothing sits still on the bottom of the pot long enough to scorch. Nothing about the process moves fast. Rushing it trades a creamy pot for a burnt one, and there's no fixing that after the fact.
The rice that gets creamy, and the rice that won't
Reach for short-grain or medium-grain rice — arborio, sushi rice, or anything sold as pudding rice — instead of a long-grain variety like basmati. Short-grain rice releases its surface starch fast, which is what thickens the pot; long-grain resists that on purpose, since it's bred to stay separate rather than fuse into whatever it's cooked in. Built on basmati, this method will simmer for an hour and stay thin no matter how much longer you leave it on the heat.
Stovetop or oven
Both methods use the same ratio and end at the same texture. They just get there through different heat. On the stove, rice, milk, and sugar go into a heavy pot over medium-low heat and simmer, loosely covered, for 45 minutes to an hour, stirred every few minutes. In the oven, the same mixture goes into a buttered baking dish at 300°F (150°C) for closer to two hours, with heat coming from every side rather than just the bottom. The oven method is slower and needs almost no attention once it's in, and it produces a thick, golden skin on top as a matter of course rather than a hazard to manage.
Keeping the heat low enough
Milk scorches long before rice finishes cooking, and it happens on the bottom of the pot where you can't see it starting. Once the milk solids catch, the burnt flavor spreads through the whole batch within a minute or two. Stirring harder doesn't undo it — the fix is starting over, not scraping harder. A heavy-bottomed pot buys some margin, because it spreads heat instead of concentrating it under one spot. The real safeguard is heat low enough that the surface only just trembles, with the occasional bubble at the edge rather than a rolling boil, and a stir every few minutes so nothing sits against the metal long enough to catch.
Eggs, if the recipe calls for them
Some versions finish with a beaten egg yolk or two, stirred in near the end for color and a rounder mouthfeel — not because the pudding needs it to set. Added straight into a simmering pot, the yolk scrambles into visible flecks within seconds, since egg proteins start to firm up around 160–180°F (71–82°C), well below what the pot is running at. Temper it instead: whisk the yolk in a separate bowl while ladling in a few spoonfuls of the hot pudding, a little at a time, so it warms gradually before it goes back into the pot. Once it's in, keep the heat low and give it another minute or two to cook through — no more simmering hard once the egg is in.
How to tell it's done
Rice pudding thickens further as it cools, so a pot that looks right on the stove is already past where you want to stop. Pull it when it coats the back of a spoon in a thin, even layer and holds a line when you drag a finger through it — looser than you'd expect a finished pudding to look. Leave it on the heat until it looks set in the pot, and the same batch turns dense and cuttable once it's cold, because the starch keeps tightening for a while after the heat goes off.
Stopping the skin from forming
A skin forms wherever the surface of the pudding is exposed to air. Water evaporates fastest right at that surface, concentrating the milk's proteins there until they coagulate into a thin film — the same thing that happens on a mug of hot milk left standing. Stir the pot every few minutes while it simmers and the skin never gets the chance to set. Off the heat, press a piece of parchment or plastic wrap directly onto the surface, not just over the top of the pot, if you want to stop one from forming while the pudding cools. Baked versions do the opposite on purpose: left alone in the dry heat of the oven for two hours, that same film gets thick enough to turn into a genuine golden crust, which is the reason to bake it in the first place if a crust is what you're after.