In that case, sounds like you're going to need a holding area. I've heard many people say they have good luck with just Rubbermaid totes (i.e. plastic bins) with air stones running in them. You might be able to rig up your current filter on one, too, instead of a stone.
Taking a lot of guesses, I'd probably suggest something like this:
A 3' tank is probably 40-50 gallons, I'm guessing (depending on the shape). Rubbermaid bins are widely available in, I think, 16 and 20 gallon sizes. So, you'll probably need three, just to be sure. Two for the fish, and one for the gravel/ornaments. If you happen to get a larger bin, it would probably be ok to put all the fish in one bin, if it's only for an hour or three. Others may disagree.
1) Get some plastic bins, and rinse/wash them thoroughly. Make sure there's no soap or detergent left in them.
2) Siphon about half your water into the bins that you're going to store the fish in. Keep in mind that 10 gallons of water will weigh 84 pounds, so the bins might not be easy to move.
2a) If you have live plants, remove them, and put them somewhere where they'll stay wet (in old tank water).
3) Set up an air stone, and/or rig your old (and new!) filter in each of the bins that you're going to keep fish in.
4) Net your fish, and place them in the bins.
5) Siphon out the rest of the water, and put it in the fish bins (except for a little bit).
6) Put your gravel/substrate and decorations in another bin. Probably wouldn't hurt to have enough water left over to keep these covered while you move.
7) Dismantle old tank.
8 ) Place new tank.
9) Add some new substrate (you're probably going to want more, if the tank is that much bigger).
10) Add your old substrate on top of that. Or, just mix the old and new substrate together, and spread it out, if you have different colors, or just feel like it.
11) Hook up new filter.
12) Put in decorations.
13) Fill to about 1/3 to 1/2 full of new, dechlorinated water.
13a) Put your plants back in, if you have live plants.
14) Add some more water, to about 3/4 full. Use either some of the old water from the bins, or fresh, dechlorinated water, or both.
15) Transfer your fish into the new tank.
16) Top off the tank.
1&) Go dry yourself off.
If you're lucky, and have everything laid out, you could be done in two hours or so. I'd probably count on four, though, especially if you have live plants.
Keeping a steady temperature may be the hardest part, depending on your home. Make sure the fresh water you add is at the right temperature, and if possible, you may want to put your heater(s?) in the bins while you make the switch. Covering the bins as much as possible while doing other stuff will help, too.
If possible, you might want to have both your old and your new filter running simultaneously for a few days, up to a week, just to make sure that you get a good bacteria colony firmly embedded in the new filter. If you can add your new filter into your old tank, and let it run for a few days (with the old filter, too), that would be an extra bonus, I'd think.
About water changes, I would also recommend a
Python No-Spill. I love mine.
