Hi your in luck we are experts at this having been showing koi at shows since 1990 and are still going strong all be it with help
You'll need a number of box's either strong cardboard or Polystreene, buy large industrial strength plastic bags large strong elastic bands and some black bin liners.
Placing one large plastic bag inside the other you then part fill the bag to just enough to cover your koi.
Next catch the koi and place it in the bag ( do you have an Oxygen bottle ) if not an air pump or air compressor ?
Grasp the top of the inner bag then pipe air or oxygen until the bag inflate to where your hand is you should have enough at the top to double it over so say 4-6" down.
Next twist the top of the inner bag until you have a balloon and double this over on itself, next tightly twist an elastic bag around the top of the double over bag if done coorrectly no air should be able to escape then do the same with the outer bag ( this outer bag is protection against leaks as koi have been known to puncture the inner bag with the rays of their dorsal fin) , yes they are that powerful.
Next place the blown up bag into a black bin liner this helps calm them down and put everything into your box .
You then place the bags across the axle of the car or van, not forwards as a sharp stop in an emergancy will cause bag burns on the nose of your koi (yes it is possible).
Repete the process ith each koi until all are loaded.
With smaller koi up to about 8" you can put more than one into a bag with the larger koi only one per bag.
Driving drive at a steady even pace (do not speed) and take any corners at a slower pace, you and your koi should arrive safely at journeys end.
Then remove the bags black bag and all and float the bags in their new home for around aout half an hour to equalize on pond temperature .
Once this is done lift the bag out f the water take away the black bag, next as gently as you can un tighten the elastic bands from the outer then inner bag and slowly pour them into their bew home
If they were new to your pond and you have existing fish you will need to QT them for a month first looking for any signs they may have an infection.
For long journeys of over 70 miles you will need to use oxygen for shorter duration journeys of around 10 miles you can use air
If you buy a bottle of stress coat by API put one or two drops in each bag or if you buy Elbagin only a few grains , the water will turn yellow dont worry it has a calming effect on your koi but only a few grains just enough to turn the colour of the water the stress coat, if you choose that option does the same job of calming your fish.
If at all you see the water turn red dont worry its a sign of stress they bleed from the gills , if they didnt they would probably die,so in this case the koi must be lifted from the bag and put straight into the pond or QT unit with no equalization of the water temperatures ( the koi will be fine)
In all our years of showing some trips over 170 miles we have not lost one koi , in that time weve had one bleeder who did it going to and from three shows after that we retired her, she is now a pet and is at the moment 27 years old
A final word of warning do not just float them in polystrene boxes or cooler boxs they are then unsupported and at a danger of either dying from a lack of oxygen or wost case senario jumping clear of the boxs.
If at all you are in the event of an accident or break down you will needa backup plan that you can rapidly swing into action
Also plan your route from start to finish factor in breaks traffic and how many hours it will take.
Remember the shortest route is the best ( its best to start in the early morning to avoid traffic).....
I hope all this helps you in your transportation of your fish good luck ,one last thing just how many miles do they have to travel please (just so I can say oxygen or air)
Dave