Transpose exchanges a stack of astral fire for umbral ice and vise versa.
You get stacks of astral fire by casting your fire spells. It makes the fire spells more expensive but also do more damage.
You get stacks of umbral ice by casting your ice spells. It makes the fire spells cheaper and you regain mana faster.

The general idea is to stick with fire as much as possible, then switch to ice to regain mana, then go back to fire.
At low level it is basically fire 1, fire 1, fire 1, .... until you can't cast fire 1 anymore, then transpose (so your stack of astral fire turns into umbral ice), cast blizzard 1, by then your mana should have gone back up or keep casting blizzard 1 until your mana is basically full, then cast fire 1 again and go back to the beginning. If transpose is on cool down (not available) then skip that part and go straight to blizzard 1.
To be extra special throw out lightning whenever it expires, usually after switching to umbral ice.

If you are dealing with 3 or more creatures close together then use fire 2 instead of fire 1.