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.

The theory of fluid and crystallized intelligence was developed by Cattell and Horn (R. B. Cattell, 1941, 1950; 1971; Horn, 1965; Horn & Cattell, 1966), who used factor analysis to show that primary mental abilities such as reasoning ability, word fluency, verbal comprehension, facility with numbers, spatial visualization, and processing speed, can be organised into two principle classes of ability: fluid intelligence and crystallized intelligence. This conceptualization has withstood the test of time, and is widely used in cognitive neuroscience today.

Fluid intelligence (Gf or gF!) broadly captures our general reasoning ability. To quote from Jonassen &  Hopkins (1993): “Gf represents different forms of reasoning including abstracting, forming and using concepts (classification), perceiving and using relations, identifying correlates, maintaining awareness in reasoning, and abstracting ideas, especially from figural and nonverbal… content” (p. 53). It has been described as the source of intelligence that an individual uses when he or she doesn’t already know what to do.

Crystallized intelligence (Gc) describes abilities depending on specific, acquired knowledge or expertise – the result of learning and acculturation. It is measured in tests of expert knowledge, general information, use of language (vocabulary) and is reflected in a wide variety of acquired, specific skills (Horn & Cattell, 1967). Educational and cultural opportunities are central to its development. Working memory capacity is closely related to fluid intelligence, and there is strong evidence that training working memory can improve fluid intelligence (Jaeggi et al, 2008).

People with a high capacity of Gf tend to acquire more Gc knowledge and at faster rates, and this has been called Gf  investment.