Get the new pot ready with soil at the bottom to match the current height of the root ball. For example, if the root ball is 8" tall and your new pot is 12" deep, put just under 4" of soil in the bottom so when you add the 8" rootball, it will be even with the rim of the pot.
Then slide your plant out of the current pot and sit it on the soil in the new pot. Fill around the sides. If you have another pair of hands to hold it steady while filling the sides, that helps, but you do do both things at the same time, one hand for each thing, if needed.