There are a bazillion recipes for miso soup on the web, but I'm going to give you mine anyway. Because it has more pictures.
Start with the dashi. That's essentially a fish stock made from kombu (kelp) and dried bonito flakes. (A bonito is a fish somewhere between a mackerel and a tuna - exactly where I don't know).
Start by soaking about 20 square inches of kombu

in 6 cups of cold water for half an hour or so.
Then start heating the water. Take the kombu out before the water boils -- when the little bubbles at the bottom of the pan start to rise to the surface. [Some people let the water come to a full boil before removing the kelp, but I've read that if you take it out before this, you can reuse the kelp 4 or 5 times. Seems to be true. YMMV.]
Take the water off the heat and add half a cup of katsuobushi.

Let it steep for five minute, then strain out the flakes. I pour the stock through a strainer lined with a folded-over paper towel.
Pour out about a cup of dashi into a mixing bowl and put the rest back on the heat.
To the stock add some tofu cut up into half inch cubes. I prefer soft tofu, but suit yourself.
Let simmer while you break up some wakame seaweed (sorry, I tossed the bag, so no kanji):

and place maybe a tablespoonful into each soup bowl. This stuff really swells up when it hits water, so be sure to break it into small pieces, no bigger than pea-size. Otherwise it looks like algae covering a lake.
Some folks say they add a little nori too (the thin sheets of processed seaweed that wrap rolled sushi), but it just sticks to my chopsticks like glue. Not advised.
Then chop one or two scallions into quarter inch rounds and add to the soup bowl(s).
Into the mixing bowl with the reserved dashi add four tablespoons of miso. Miso is a paste of fermented soy beans and rice or barley. There are a number of different kinds of miso, but the main two are white (shiro) and red (aka). I like them both. [Quick article on miso here.] Here's the white miso:

Blend the miso into the dashi until there are no clumps.
Take the dashi off the heat and let it cool a bit. Miso afficionados say that if you add miso to boiling liquid, it destroys a lot of its health benefits and changes the taste. I'll take their word for it.
Add the miso/dashi to the pan and mix well. Pour into soup bowl(s) and mix to blend the scallions and wakame.
VoilĂ !

I find that dashi keeps well in the refrigerator for about a week. So you can make a large batch ahead of time.