I used to eat Gyoza in Paris with my Uncle on Rue Sainte-Anne which is loaded with Japanese restaurants, and I love them, as I do dim sum. I actually wanted to make dim sum but bought the wrong wrappers from the thai supermarket, gyoza ones are thicker and round.
Anyway I watched this hilarious video in Japanease on youtube of this woman making them and the technique to fold them, and it worked a treat, they were very easy to do and came out perfect. I would only do them if you have lots of people over or if your happy to fill the freezer up and have time at hand to do the wrapping.
My recipe is very vague because I looked at a few and played around with what I like and tested and adapted the mix until I was happy. So add more or less and fry a bit to test.
1 or 2 packs round dumpling wrappers, I used mine all up so get another pack as they freeze well.
400g minced pork
200g raw peeled prawns chopped roughly
4/5 sliced whole spring onion (stalk included) or Chives
5cm knob of ginger chop until its as fine as you can get it
1 garlic clove finely chopped
2 tbsp chopped fresh coriander
around 4/5 water chestnuts chopped up smallish, not too small or you wont really notice them,
1 egg mixed with fork
2 tbsp soy sauce
Rice wine vinegar
A few drops sesame oil
If you have a hand blender use it for a second on the pork mince just to make it a bit easier to mould, then add all the other ingredients to it, lastly add the egg, you probably won't need to use all the egg so just add a little at a time until it all comes together, the egg is only in to hold the mix together so it doesn't crumble out when you cut them in half.
I was about to write a blurb on how you put them together and cook them but the easiest thing to do is to watch the video and then have a go. http://www.youtube.com/watch?v=spsGbDWauf4
To cook them like I did, boil them in simmering water until they rise to the top, then fry in a hot pan and couple of tbsp's of veg oil until they are golden brown. Serve with the rice vine vinegar.