Right, this is something I've had to dial in properly for my static caravan setup, so worth sharing what actually works.
Resting voltage first
Switch everything off and leave the battery alone for at least an hour. No chargers, no loads. Then measure across the terminals. A healthy 12V LiFePO4 should read between 13.0-13.4V when fully charged. Lead-acid will be around 12.6-12.8V. If you're getting significantly lower, you've either got a discharge issue or the battery's knackered.
Under load test
This is where you'll spot real problems. Turn on a moderate load (caravan fridge, some lights) and measure again. Healthy cells hold voltage. If it drops more than 0.5V, you've got internal resistance issues — usually a sign the battery's degrading.
Check individual cells (if accessible)
For lead-acid, you can test cell voltage if the caps come off. Should be roughly equal. Wild discrepancies mean that cell's failing.
Watch the meter response
A quality multimeter (I use a Fluke) will give you stable readings on a healthy battery. If the needle bounces around or the digital display flickers, that's a red flag for connection issues or a dying battery.
Temperature matters
Cold batteries read lower. Test in normal conditions if possible. I've learned this the hard way during winter mornings.
The multimeter's a starting point, not the full picture mind you. For lithium, you really want to monitor with a decent BMS or something like a Victron BMV. But basic voltage checks catch 90% of problems.