In the United States, a parent can request that their child be tested by their school district. In most states and most districts, they do a "blanket" testing at some point. In my school district, we test all second graders. This is because the tests are more likely to produce accurate results at this age. Parents can also request testing.
If testing by your local schools is not an option, or if you home school, you still have options. You can see a child psychologist and request an IQ test or evaluation. This is the most costly, in my experience, but can be the most accurate. It also gives you a better holistic picture of your child as a thinker. Be careful in who you choose; some doctors will say all kids are gifted as that is what most parents want to hear.
Another option, which I highly recommend, is to have your child tested independently. If you know a certified teacher, they can act as a proctor. You can order the CogAt and have your child tested. They will then send you the results. This will help you see your child's strength areas, as well as whether they are significantly asynchronous in their giftedness. Asynchronous intelligence is very common, so don't fret if you see high scoring in one area and low scores in another.
The CogAt is a very commonly used test for giftedness that measures a child's percentile against age-level peers. It is controversial as well. It is frequently used because it is inexpensive, it can be group administered and because it tests in three separate areas. Testing in three separate areas is required by most school systems. It is controversial because it appears to be biased towards majority populations. Additionally, many gifted students do not test well on it, which causes false negatives.
There are a host of other tests that can be conducted; these are just the two types of testing that I see most often.
For my Canadian friends, I found these two gifted resources that might give you information more specific to your nation.