The steps involved are:
* Write the skeleton equation
note: you know the silver carbonate is the precipitate(s) because nitrate compounds are always water soluble
*Write the (aq) compounds show show the ions have been pulled apart by the dissolving properties of water
*Identify spectator ions which exist in the dissolved state as both reactants and products and cross them out then re-write the remaining ions and precipitated compound.
Now balance number of ions and charges to find the final answer shown at the top.
Here is a video which gives another example of how to write a net ionic equation for a precipitation reaction.
Hope this helps!