For the UK you are looking are Royal Mail Special Delivery as one option. Officially fish are not allowed but fry are on the restricted list so are ok as long as you mark the box "Urgent - Living Creature - Handle With Care"
Some people will not send fish via Royal Mail for certain reasons (some claim they are box jugglers) and if that is the case you could look at APC (which I think are licensed animal/fish couriers)
There's probably others over here, but I'm not sure. I've not had many problems with Royal Mail so use them for now.
For shipping them I would use a polystyrene box or cardboard box lined with polystyrene (you can cut larger sheets from B&Q or wickes to fit).
Using a heat pack is advisable, especially with tropicals and packed with something to help insulate them (poly chips or shredded paper)
Double bag them and tape up the corners of the inner bag to stop them getting stuck in the corner. I usually have about 40-50% of the bag filled with water, the rest is air
Don't blow into the bag to fill it when tying it, as your breath will have co2 in it.
Probably no real benefit but I ship them in 50% current tank water and 50% fresh (tank ready) water
Don't feed them 24hrs before transit, so they produce less waste during the trip. Properly fed fish will easily survive not being fed until they arrive at their destination
There's probably plenty more things, and the tutorials will undoubtedly be of help
