If, for example, I wanted to say "I like the book that my sister gave me",
would it be `姉がくれた本が好きです`?

I'm using Genki to study, but they don't seem to have any examples of this
particular structure that ends in "が好きです".
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particles relative-clauses
Is it OK to have more than one が particle in a sentence?
Yes. You have two nominative noun phrases in your English sentence, one in the
main clause and one in the relative clause. Japanese is no different.
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Yes, these `が` particles mark the subjects for the following verbs, so you can
use `が` to create [relative
clauses](http://en.wikipedia.org/wiki/Relative_clauses). (There are other `が`
particles in Japanese, such as the phrase-ending version).

Note that `は`(topic-wa) does not work this way, but most of the other
particles that mark a noun do, such as `を`,`で` and `に`.
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Yes, 「姉がくれた本が好きです。」 is correct.

The first が, because it is in a clause that modifies 本, can be also be swapped
with の. So 「姉のくれた本が好きです。」 is also correct, and has the same meaning.

This is not the only reason that が can appear multiple times in a sentence.

Predicates like 好きだ are called "double-ga" or "affective" predicates1. This
class also includes 分かる, いります, and できる, and all of these take が instead of を
for the equivalent of the English direct object. So if you ask,

> だれがお姉さんがあげた本が好きですか。

The answer could be,

> 僕が姉がくれた本が好きですよ。

This has three が, and only one of them is in a relative clause. This also
implies that the other people don't like the book.

**Footnotes:**

1: This is the terminology used in "Japanese: The Spoken Language". Your text
may use different terminology.
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