I did some research on the net but I still don't understand the 'secret' to making them look glamorous like the shops do them.

Is the proper way to cook them, to steam them within the shell in some rice cooker?

My other question is, do Japanese people make poached eggs in any dishes?

The poached and onsen tamago seems to have difference taste. FYI, I can't seem to get poached eggs right either (even with lots of swirls and vinegar).

This person has tried:
1. Wrap a few eggs (out of the fridge) in two layers of rather thick kitchen paper, sprinkle some warm water (from your kitchen heated tap water... meaning not too hot) to bring the eggs to room temperature.
2. Boil some water in a saucepan, when it comes to boil, turn off heat, and place 1 in the water and put the lid on.
3. Let it sit for 15 minutes then it's ready.
4. This 15 minutes is for winter, and for people who prefer to have the egg yolk half-cooked too.
5. Try a few minutes shorter in summer).
(6. is some suggestion for a sauce.)

The key seems to be to keep the eggs in 65 degrees C water for 20 - 30 minutes. Because the moisture in the kitchen paper lowers the hot water temperature, the heat from the pot does not directly reach the eggs, so it works.

Now just need to get some kitchen paper that doesn't disintegrate easily :(

To do this at home, all you have to do is to find something that can maintain a fairly hot but not too hot temprature for a long enough time.

There are onsen-tamago-makers available, but you don't need this. You can put a raw egg into a thermos full of hot water overnight, and you can have a nice onsen-tamago in the morning.

Or what I do is to put a raw egg inside a rice-cooker that is warming rice. What I mean is, don't put the egg in as you are cooking rice. But after the rice is done, most modern rice-cookers automatically switch to "ho-on" mode where the cooker keeps the rice hot. Put the egg in there. Keep the egg in for about 40 minutes, and your egg will be perfect. If you wet the egg just before putting it in the cooker, it will prevent the rice from sticking to the egg. If you leave it there longer, it turns into a tasty hard-boiled egg, btw.

Cooked it too well. I think I'm getting the hang of it.

I am trying the warm water method first by the way, as I don't normally cook or eat rice.

Temperature control is the key - you must use a thermometer.

Set eggs out to room temperature for half hour or so.
Heat water to 62 degrees centigrade, add eggs.
Over the next 25 minutes or so, raise the temperature to 72 degrees centigrade. Do not go over 72 degrees.

After 25 minutes, remove eggs, put in cool water for about a minute, then take out and set on counter.

Crack eggs open into individual dishes, add about 2-3 tablespoons of dashi (I use bottled liquid dashi called shiro dashi - Shichifuku brand - thinned down with a bit of water) and serve. Optional garnish – chopped green onion.

I will try it this week and will report back, hopefully with some pictures.

Do not let the water come to full boil. A bubbling slow boil just before full boil is best and should be maintained. I believe its called insipid boil.
This will cause the white of the egg to wrap nicely around the yolk while cooking. A full boil will make the egg want to break up and turn into a nasty soupy pot of water.