Where do I find kilowatt-hours per year?

The yellow EnergyGuide label on new units, and the manufacturer's spec sheet or model lookup for the old one. Failing that, a $25 plug-in meter measures it directly in a week.

Does this account for the old unit's remaining value?

No. It compares running costs only. If the old unit still has resale value, subtract it from the purchase price.

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Is replacing that old appliance worth it?

Replacing a working appliance only makes financial sense when the energy saving repays the purchase within a reasonable share of the new unit's life. The two numbers you need are on the yellow EnergyGuide label: estimated kilowatt-hours per year for each machine.

Old unit, kWh per yearNew unit, kWh per yearPurchase price ($)Your state

What to know

Payback under about five years is usually worth doing on an appliance with a 12-to-15-year life. Past ten years, the old unit will often fail on its own schedule and the calculation is really about convenience.
Rebates change this sharply. Subtract any utility or federal rebate from the purchase price before running the numbers.
If the old appliance is a second refrigerator or freezer, consider retiring it rather than replacing it. Zero kWh beats any efficiency rating.

Questions

Where do I find kilowatt-hours per year?: The yellow EnergyGuide label on new units, and the manufacturer's spec sheet or model lookup for the old one. Failing that, a $25 plug-in meter measures it directly in a week.
Does this account for the old unit's remaining value?: No. It compares running costs only. If the old unit still has resale value, subtract it from the purchase price.

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