People watching is pretty much what it sounds like in British and US English - observing people's actions and interactions, not to be creepy but because it can be funny to only get the external view of what's going on with no other knowledge, or it can be relaxing to watch the world go by
The verb piacere means "to be pleasing." So the subject of the sentence is not the watcher (io) but the action of watching.
"Mi piace guardare la gente." = "To me, people-watching is pleasing."
It is only when we rephrase the sentence into "I like people-watching" that the subject becomes "I."
I think you are asking how to translate "I like people-watching" into Italian. The natural Italian translations are
"Mi piace guardare la gente," and
"Mi piace osservare la gente."
Italian simply does not have a verb that works the way "to like" works in English. There is "volere" = "to want," which (in the conditional tense) works in sentences like
"Io vorrei osservare." = "I would like to watch."
But to say simply, "I like to watch," you have to use "piacere," with its reversal of the roles of subject and (direct/indirect) object:
"Mi piace osservare." = "I like to watch."
I hope that answers your question.
In case you are still interested, here is what I meant:
The subject of the Italian sentence is "guardare la gente" which is a verb phrase, an action. We can translate directly into an English sentence keeping the action of "people-watching" as the subject:
- Italian: Mi piace guardare la gente.
- Englsh: To me, people-watching is pleasing.
In both the original Italian sentence and this direct translation, the actor -- the person who does the watching -- shows up as an indirect object, "mi" = "to me."
In English -- but not in Italian -- there is another natural way to express the same idea:
- I like people-watching.
In this sentence, the subject is "I" and the action (gerund) "people-watching" is the direct object of the verb "to like." But there is no corresponding Italian sentence with subject "io."
Whew . . . I hope that covers it.
Was "I like people-watching" accepted? In that sentence, "people-watching" acts as a noun; however, there is this English rule that you should not split infinitives, for the second sentence. This is why you cannot split "to watch" and say "I like to people watch;" it must be "I like to watch people."
To put it simply, there is no such rule. The existence of such a rule is a widely held belief not supported by linguists or grammarians -- in other words, a myth.
Besides, "to people-watch" is not a split infinitive. It is simply the infinitive of a verb meaning to engage in the activity of watching people in a public place.
A couple references on the split infinitive construction:
Because "gente" is a singular, feminine noun. Singular nouns ending in 'e' can be feminine or masculine. The plural forms of (almost) all such nouns end in 'i':
- il fiore, i fiori = the flower, the flowers
- la gente, le genti = the people, the peoples
Note, however, that in the particular case of the word "gente," the plural is very rarely used in modern Italian.