the key issue is the filters, it depends a little what your plans are regarding filtration how it's best to do it. You have a few options
1 - if you intend to just use the current filter on the new tank then just transfer it over, make sure you keep the filter media wet during the change over, if it's an internal then sit it in a bucket of tank water, if it's an external just make sure it's still full of tank water.
2 - if you intend to use a new filter (or the 2nd hand one) on the new tank you can either
a - do a complete fishless cycle on your new tank, this may take some time and would only create a 'cycled' tank rather than a 'mature' one.
b - run the new filter alongside your old one in your old tank for a couple of weeks to build up a bacteria colony
c - transfer over the media from the old filter to the new one and set it up on the new tank straight away
d - run the new and old filters in tandem on the new tank for a couple of weeks to build up a bacteria colony.
Ok so aside from filter issues it's pretty easy to change over fish from one tank to the other.
1 - turn off the filter, heater, lights etc on the old tank, unplug everything
2 - start siphoning water out from the tank
3 - while it's draining remove all tank decor
4 - keep 1 (or more depending how many fish you have) big bucket of tank water, start netting your fish when the tank's about 2 thirds full and put them in teh bucket, when you've got them all cover the bucket with a towel
5 - finish draining the tank, sling the water, you don't need to keep it, just as long as you keep your filter media it'll all be ok.
6 - set up the new tank wherever it needs to be, put the heater and filter in place but don't plug them in
7 - fill the tank with water (make sure you use dechlor) when the heater is covered by water then turn it on
8 - when the filter inlet and outlet are covered turn that on too
9 - leave the tank to come up to full temperature, this won't take too long and gives you a chance to check all the equipment etc is working correctly
10 - add your fish
11 - don't feed that day as they'll be stressed and probably won't touch it, then you'll have waste in your tank and could pollute the water
12 - make sure you do water tests the day after to check everything's OK.
Good luck