Being one of those former "gifted" kids myself, I'm going to give a few suggestions. I'm trying to be polite -- I'm just wearing a few chips on my shoulders. Keep in mind that, if I get a little bit snarky, it isn't at you.
I can only put this frankly: be extremely sure that, in trying to find out, you have the child's best interests at heart. So many parents think, however unconsciously, that having a gifted child is another kind of status symbol that they can flaunt around. It absolutely isn't. Parents also tend to heap unrealistic expectations regarding academic performance on the child. I promise, by doing this, you'll only cause the child to lose all interest in his or her studies. I've seen more than a few of my fellow "gifted and talented" students drop out of school.
Don't ever call the child "gifted". Don't call him or her anything. They'll be able to figure out for themselves that they're different than other children, and in exactly what kind of way. If you dote over their abilities, you're likely to give them too much cocksure confidence in them, and that isn't helpful or healthy. They need to learn their abilities and limits on their own. Also, trust me when I say that, by the second grade, "gifted" carries the same stigma as "retarded". Students do not enjoy it when one of their classmates becomes a teacher's pet (this sometimes happens). Teachers sometimes do not enjoy having "gifted" students (this happens just as often). In either case, whoever is offended by the child will lash out at him/her.
Finally, you have to understand that children need to be children. It is not important at all that the child has some kind of long record of outstanding academic or artistic work. If the child doesn't want to study, don't fight any harder to make him or her do it than you would with any other child.
I've seen a lot of parents try to live vicariously through the success of their children, and a lot of undue expextations placed on gifted children. I've seen a lot of child prodigies rise to excellence, only to have them vanish without a trace shortly after.
I was in a lot of those G&T schools and programs when I was young. Most of the students either dropped out of high school or didn't do anything after they graduated from high school. Two of them killed themselves, and one is in prison. Some, but not all, of those who are left are rather unable to interact socially with other people in a normal setting.
Now, there is some benefit to knowing whether or not the child has an above average set of talents. If the child is doing poorly in school, it's a very good idea to arrange an IQ test or an aptitude test of some kind before you let the school counselor scream "ADHD" at you (actually, as a rule of thumb, no matter what your school's counselor tells you, you should blow it off and remind her that she didn't make it into graduate school with her BA in Psychology and marginal GPA, and also doesn't know what she's talking about). It's possible that the courses aren't being paced quickly enough. That does NOT mean that you should give the child more of the same work just to keep his or her pencil moving all of the time. And never, EVER make the child feel as though her performance is tied to how much you care for her.
I guess the answer is, as long as the child isn't suffering academically, don't worry about finding out whether or not your child is gifted. I'm doing fine (I'm working on a doctoral degree, and I'm teaching math at a university), but I'm still pretty angry at a lot of people.