On their migrations birds sometimes frequent very different environments from those in which they nest, and a study of the migratory birds alone might be very misleading to one endeavoring to classify birds ecologically.
I imagine you're confused by the fact that nest, which you are likely to be familiar with as a noun, is used here as a verb.
As for how to identify the verb—by and large, it will be the first non-adverbial constituent after the subject. In this particular case, you parse the relative clause something like this:
... in which they nest
You know immediately that the relativizer which is the object of the preposition in, because the preposition is right there in front of it. A preposition phrase is very very unlikely to act as subject of the clause; it can't be the verb; it is probably an ordinary locative indicating where something happens . . .
. . . so the next constituent of the clause ought to be the subject. They is unambiguous here: it's a personal pronoun in subject form, so it has to be the subject of something, and it's a pretty safe assumption that what it's the subject of is the relative clause. Consequently . . .
. . . the next constituent should be the verb you're looking for. It might be preceded by an adverbial of some sort, so you have to be ready for that; but in this case a glance at what follows suggests that the relative clause actually ends after the next word, nest, so nest pretty much has to be the verb, despite the fact that you know it as a noun. You turn to your dictionary (I'll use Collins because it's on the top of my list of bookmarks) and Behold! you find as the second definition:
When a bird nests somewhere, it builds a nest and settles there to lay its eggs.
- Some species may nest in close proximity to each other.
- ...nesting sites.
The same sort of analysis (but without the complication of dealing with a relative clause) will show that the verb in the main clause is frequent (Collins again):
If someone frequents a particular place, they regularly go there. [formal]
- I hear he frequents the Cajun restaurant in Hampstead.