This could be the most frequently asked question from parents (and teachers too).
Gifted children have high ability and, while there are many definitions and many ways to identify giftedness, the single best indicator would be a standardised test, properly administered and interpreted by gifted-friendly professionals.
Parents could consider compiling a profile on the child's ability and achievements for negotiating with schools for planning appropriate education programs and strategies to be used for a gifted child throughout the compulsory years of schooling.
Standardised test results help with determining what educational programs each gifted child needs. Ability tests are as follows. WPPSI is used for the very young, and for older children there are two suitable Stanford Binet tests: SBLM and SB5. Also there's WISC4, and perhaps Raven's non-verbal should be considered too. These are all regarded as accurate tests to use with gifted children.
For your information, incidence and categories of giftedness (IQ scores) that some refer to are:
Mildly (basically) gifted 115-129 (1:6 - 1:40)
Moderately gifted 130-144 (1:40 - 1:1000)
Highly gifted 145-159 (1:1000 - 1:10000)
Exceptionally gifted 160-179 (1:10000 -1:1million)
Profoundly gifted 180+ (<1:1million)
[Silverman, Gross (et al)]
Should you need to look at private testing, seek out a psychologist experienced with gifted children.
High ability doesn't guarantee high performance particularly for children whose ability is not recognised or appreciated by those who influence the child's development. Be cautious about revealing test scores to people who don't know anything about giftedness.
Of course there are gifted children who need different forms of identification too. Anyone can access and use the Saylers Checklists recommended by Education Queensland to identify giftedness. There is also a good checklist for parents among the Sayler's material.