I will consider you are moving everything (Gravel, decors, etc). and the new tank has it's filtration system set.
1- Turn off the filters, heaters, etc... Wait at least 15 minutes for the heater to cool down. Drain as much tank water in a large plastic clean container.
2- Take your fish/inhabitants with a net and move them to this container.
3- Drain the rest of the water. In this step, do your best to vaccum the gravel to remove as much dirtinnes as possible.
4- If you have live plants, make them float in the plastic container. Aquatic planst will dry out in minutes if left on dry air.
5- Start moving the gravel with a cup or a large spoon. Put a towel in the floor for this will drop a lot of water.
6- Add your new pre-washed gravel (since I think you'll need more)
7- Move/add the decors, and set them the way you like.
8- If you have live plants, add some water from the container until the gravel is covered. Start planting them. DO the same if the plants are plastic.
9- Move some of the container water to the tank, being careful to not bring the debris (mostly poop) that is in the bottom of the container. The more water you can move, the better.
10- Fill the tank with clean dechlorinated water.
11- Wait 15 minutes, start the filters and heaters.
12- Move the fish to their new home.
These are the steps I've taken when I moved everything fom my 20 gl to a 50 gl.
Now, let's talk about filtration and temperature.
If you have heaters, it's important that you unplug them 15 minutes before lowering the water level, and then wait 15 minutes when you move them from one tank to the other before you plug them.
About the filter: it's importantthat you don't discard your previous filter media. If you are using a power filter (Hang on back, canister, etc...) you should let it running in the new tank along with the new one for around 4 weeks, to help the biological cycle of the new tank. Also, if it has sponges / floss pads, you can put those in the new filter along with new media. Both ways will help you and your fish. In case you are using an undergravel filter, you already did this when you moved the old gravel to the new tank.