The precept is very clear:
I undertake the training rule to abstain from false speech.
Musāvādā veramaṇī sikkhāpadaṃ samādiyāmi.
Musāvādā comes from two words: musā, which means neglectfully, falsely, or wrongly; and vadati which means to speak. Musāvādā as a noun simply means "a lie". The language is clear: this precept means not to tell lies.
If you are asked how you are and you respond with "I'm fine" when you're not fine, you've told a lie: it is false speech.
If you say food tastes delicious but it really doesn't, you've told a lie: it is false speech.
Do these "white lies" break the precept? By the simple language of the precept, yes. One might tell these kinds of lies to avoid giving lengthy explanations of our health or moods, or to avoid offending someone when we don't like their cooking. But to lie is to break the fourth precept, regardless of the reason for the lie.
What can we do? Use a skillful approach to responding that does not require telling a lie. "How are you doing?" even if you are miserable can be answered with another truthful statement, such as "Oh, I've been very busy" (assuming you've been very busy). "How is dinner?" could be answered with "I'm enjoying it greatly" if you are in fact enjoying it (which isn't the same thing as liking the taste specifically; it's entirely possible to enjoy a meal without liking the taste if you're enjoying other aspects of the meal, such as the opportunity to be with friends and family, or perhaps the opportunity to eat mindfully and regard the flavors of the food even if they're not your favorite).
To follow this precept is to keep your speech pure. If the precepts were easy to follow, we wouldn't need them! Avoiding false speech requires great skill and thoughtful responses, but we can all do it.