Excellent definitions from Kevin S. McGrew in Intelligence 37 (2009) 1–10. You can’t get much more up-to-date than this.

Fluid intelligence (Gf): The use of deliberate and controlled mental operations to solve novel problems that cannot be performed automatically. Mental operations often include drawing inferences, concept formation, classification, generating and testing hypothesis, identifying relations, comprehending implications, problem solving, extrapolating, and transforming information. Inductive and deductive reasoning are generally considered the hallmark indicators of Gf. Gf has been linked to cognitive complexity which can be defined as a greater use of a wide and diverse array of elementary cognitive processes during performance.

Tests include: General sequential (deductive) reasoning, Inductive reasoning, quantitative reasoning, speed of reasoning

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Crystallized intelligence (Gc): The knowledge of the culture that is incorporated by individuals through a process of acculturation. Gc is typically described as a person’s breadth and depth of acquired knowledge of the language, information and concepts of a specific culture, and/or the application of this knowledge. Gc is primarily a store of verbal or language-based declarative (knowing what) and procedural (knowing how) knowledge acquired through the investment of other abilities during formal and informal educational and general life experiences.

Tests include: Language development, Lexical knowledge, Listening ability, General (verbal) information, Information about culture, Communication ability, Oral production and fluency, Grammatical sensitivity, Foreign language proficiency, Foreign language aptitude.