Easy! I steam fish about 1x per week with a bamboo steamer. You need to take advantage of the steam rising from the pot which can steam your fish in exactly the same way as the rice cooker - so you get a Bamboo Steamer like this one (available in tons of different places, including cooking-supply stores, Asian Foods stores, etc): http://www.amazon.com/Norpro-Deluxe-3-Piece-Bamboo-Steamer/dp/B00005EBH8
This steamer is basically open at the bottom (with bamboo slats) so you set this on top of the boiling pot, and it fills with steam, cooking the fish. It's recommendable that you wrap the fish in wax paper (I use baking paper in a pinch) and that will keep it from sticking to the bamboo.
Hope this helps! I recommend buying a bamboo steamer like this one - it's a common kitchen item that you can use for a ton of steaming - i.e. veggies, broccoli, fish, etc. No need to even be cooking rice - you just place this over a pot of boiling water, and it works great!
Assuming plain (American) white rice on a stovetop:
(Generally, American rice does not need rinsing for these applications)
From your description, it sounds like you are going for Steamed Rice; for that, here's what you want to do:
Bring your water, salt and butter to a boil, then add your rice. Stir it until it comes back to a boil. As soon as it boils again, turn your heat way down. Keep stirring until the heat is low enough that you feel safe that you can cover the pot without it hard boiling again. Cover and keep on low to medium-low heat or a moderate simmer (preferably without peeking) for 20 minutes (15 minimum). It is the steam that plumps the rice, so don't lift the lid! It may take some tweaking depending upon your specific equipment, but try to be patient. You may find that you like a little less water and a bit more time. When you do peek (hopefully after at least 15-20 minutes have passed) look for the water to be gone and for little holes or "divots" to be formed on the surface of the rice. If you still have water, cover again and keep cooking without lifting the lid for at least 5 more minutes. When it looks done, turn off the heat but still don't stir, you're better off just letting it sit for another 5 minutes - re-covered and with the heat turned off, then stir/fluff it.
If you find that your rice isn't done after 20-25 minutes with the lid on, bring up the heat a bit, but be careful. If your heat is too high, your rice can burn on the bottom. Within reason, if it's just a bit too low, it'll just take longer.
The lid is really key here. Do you have a tight lid for the pan that you are using? If not, we can help you improvise.
A slightly different method using the same ingredients is the Pilaf Method shown here in a great video from the love of my life, Alton Brown. 20 Minute Pilaf See the rice just before he fluffs it with chopsticks? Those are the holes/divots I referred to above in the explanation of the steaming method. In case the link goes bad, here's a description of the video: Bring 3 cups of water to a rolling boil. Meanwhile, in a saucepan with a tight lid, melt and lightly brown 2 Tbs of butter over high heat. Add 2 cups of rice (regular long grain, basmati or jasmine recommended) and saute for a couple of minutes, add 1 tsp salt (Alton uses kosher). When the rice smells "nutty" add the boiling water all at once (careful, it will boil rather violently). Cover and turn heat to low. No peeking, cook on low for 15 minutes. Fluff with chopsticks or a fork. Cover again for 5 minutes, no heat.
Note that Alton's pilaf also requires a tight fitting lid. If your lid isn't tight, try using aluminum foil to get a tighter seal.
Finally: With very small variations, these two methods of cooking rice will work fine for just about any type of rice. Some rice, particularly some rice harvested outside of the US should be thoroughly rinsed first. Check your label if you can or revisit this question if you're not sure if your rice should be rinsed. If you use rinsed rice you may find that you want to use slightly less water for cooking than instructed here.
You're using a 2 to 1 ratio for steaming rice, that's fairly typical but you might like a bit less water, just don't go lower than 1.5 to 1.
Brown rice works fine for these methods too but will take longer and require slightly more water.
The steaming method, particularly if you wait to "fluff" will produce a stickier rice, better for chopsticks :) and better to accompany food that has a sauce you want the rice to soak up. I prefer steamed rice to go with stir-fries, for example.
The pilaf method, particularly with medium to long grained rice will produce more individual grains. Nice with steak or baked chicken, something that isn't sauced.
Best Answer
I can see flaws in the method. Adding water by 'depth' is pretty inaccurate unless you use the exact same rice quantity in the exact same pan as the recipe author. Also, bringing it slowly to the boil like porridge is very inaccurate for your timings.
Let's try it a slightly different way. Use ratios & a flash-boil.
There's no absolutely ideal 'works for everybody' ratio as it depends on pan thickness, tightness of lid & stove heat. You'll end up between 1:1.5 and 1:1.75
Though this takes a lot of text to explain, it's actually really, really simple to do & once you have your ratios right for your kitchen, it will 'just work' every time.
Put the kettle on.
(This works best if you live in a 240v country, otherwise you might have to wait a few more minutes before you start 2;)
Using a small-ish saucepan with a tight-fitting lid & the heaviest base you have, pre-heat at full power as the kettle's coming to the boil. The idea of this is that the pan is hotter than the water as it goes in… but not on for so long it's glowing, or you can smell burning teflon;)
Add 1 cup of rice to the pan as it's heating (cup, mug, measuring jug, doesn't matter so long as you use the same measure for the water. That way we're working percentages/ratios not inches). Don't bother to pre-rinse unless your rice is particularly dusty. Supermarket rice really doesn't need it these days, & pre-rinsing will change the flash-boil reaction.
Add salt now if you want salt.
Add a cup and two-thirds (middle of your ratio spectrum) boiling water. The water & rice combo will immediately flash-boil almost out of the pan. Immediately drop the heat to minimum (assuming gas, or take the pan off the ring for a few seconds if electric or anything not instant) Stir once with a spatula, just enough to know the rice didn't clump, which it shouldn't if the water flash-boils on contact.
Put the lid on. (First time, until you get used to this, keep an eye on it to make sure it's not going to boil over as the initial heat drops away)
Simmer for 15 mins, without lifting the lid to check.
Don't be tempted to lift the lid to see if it's done…
This is a Schrödinger/Heisenberg* method - see below;)
This depends on your pan thickness & how low your ring goes. You learn this through repetition; after that, time it.
While you're learning the timing, then you'll have to just lift it slightly & briefly every minute from 12 or so. Once you've got the ratios for your pan/stove combo you don't do this.
Whilst you're learning at the lid lift stage, you're listening for a 'crackling' sound. That's the indicator your very last bit of water is evaporating off the pan base.
Switch off the gas (or for electric switch off & move the pan to a cold ring)
Leave 15 mins more. Don't lift the lid at all.
We don't need Schrödinger for this bit - the cat is alive;)
'Fluff with a fork' as they always say - or if you got it just right, a quick once-round with a spatula will do it. it won't have stuck.
Profit… or adjust your water ratio/timing/heat for next time.
A lot of this is learning your specific pan/stove. If your ring is hot or your pan is thin, you have to adjust your water ratio up slightly, so you arrive at the 15 minute mark as it crackles. This can mean you end up with a ratio somewhere between 1:1.5 & 1:1.75 If you err, err on the side of dryer.
Glass-lidded pans can take a lot of your early guesswork out of it, as you can see what's going on.
*Schrödinger's cat is a famous thought experiment. You don't know if the cat is alive or dead until you open the box.
We're additionally hampered in this by Heisenberg's Uncertainty Principle - that by the mere act of observing an experiment, you change the result.
Hence, you cannot know if it is done until you lift the lid… but by lifting the lid to see if it's done, you change the time it will take & the amount of water required for it to be done.