Carriers like Verizon or AT&T often offer "free" phones with a trade-in. This is only the "cheapest" way if:

Buying a new phone doesn't have to mean dropping $1,000 upfront. If you’re looking for the absolute cheapest path to an upgrade, here is the hierarchy of savings:

Note: If you have a cheap prepaid plan, switching to a major carrier just for a "free" phone usually costs you more in monthly fees over time.