Ive moved my tanks and fish twice and have done so without any losses or upsets to the water quallity.
First thing you will need are enough plastic bags to bag each fish or if they are very small 3 fish to a bag and extra ones to bag your filter media, you will also need polysterene box/s to put the bags into and something to hold all the gravel and any tank ornaments. Moving fish loosely in containers is not recomended as the fish get thrown all over the place and get injured. Bags and boxes can be got usually for free at any good lfs.
Fill each bag about 1/4 of the way full before placing the fish into the bags and tying them up trapping as much air in the bag as possible, DO NOT BLOW INTO THE BAG TO INFLATE IT! Do the same with the filter media. Once you have all your fish and media safely bagged place them upright into the polystyrene boxes so they cannot fall over and seal the box up with tape. Next place all the gravel and any tank ornaments into a large bucket with a lid or water proof bag that can be tied up, the gravel etc must be kept as damp as possible to prevent the bacteria from drying out and dying. If you are moving to a area with a different tapwater supplier you will also need to keep at least 1/2 of your tankwater to prevent the fish from dying of pH shock.
When you arive at your new home make sure the tank is the first thing you deal with, get the tank set up and the gravel replaced, then refill your tank with either tapwater (remember to warm this up with kettles full of boiling water as you go) or the water you have brought with you. To stop the water from being dirtied by the unwashed gravel pour the water slowly onto a large plate placed on the substrate. Once the tank is refilled and up to temperature break the seals on the boxes and float the bags of fish in the tank for 1/2 a hour, the media can be put straight back into the filter housings and the filters switched on.
Once all the fish are back in the tank switch off the light and cover the tank with a sheet or towel and leave it over night, dont be tempted to peak as they will already be stressed from the move and will need time to calm down. Dont feed for two days to allow the bacterial colonies to rebuild themselves without having additional ammonia/nitrites to deal with.