Carefully! I have lifted small to medium citrus out of the ground and moved them to another location multiple times... as well as into pots. And I am about to start re-arranging them on my hillside due to changed needs. So here are some things that i have learned:
The most important thing is to dig as far / wide as you can (out to the dripline / edge of the canopy) and take as many of the roots as you can. Dig carefully so as to minimize cutting/damaging/disturbing (feeder) roots. I use a pitch-fork rather than a shovel to dig. And several shovels to lift the root ball up from the bottom.
If its a large tree, you want to lift the feeder roots out of the ground and get them into the top layer of the pot if you can. (of course this depends on the pot size and roots). If the tree is small, this task should be pretty easy, try to get the rootball into the pot as intact as possible.

It will be your choice as to how much ground soil to keep, what soil or planting mix to use in the pot. I have kept one with most all of the ground soil in the pot and also done this keeping 1/2 the soil in the pot and adding a fast draining mix. To me there has been no difference in growth / performance except that i need to water the fast draining mix more frequently. It should be noted that my pots spend 99% of the time outdoors, (I take them inside when temps are supposed to dip below 25F).

BTW: the trees may or may not drop a good portion of the leaves. If the leaves drop, be patient while the tree rebuilds the root system.

Good luck!