As a parent, former gifted student, and teacher of gifted students, I think you are all off to a great start. Hoagies is the place I send parents to the most. It is a great starting place, will a lot of information and links.
I think this sticky should also mention that parents cannot do anything to make their children be more gifted. There is no evidence to show that early exposure to classical music, flash cards, books, etc will do anything to boost intellect. However, there is a lot of evidence to show that parental attention boosts brain development, particularly if that attention is positive and focused on the child. In other words, you cannot just park your babe in front of Baby Einstein and expect that will create a genius.
I think is is also helpful to point out that there is no real consensus on what it means to be gifted but that in schools gifted is equated with high intellect and high test scores. One could, of course, have a debate of semantics on what it means to be gifted, all children have gifts, what about other gifts, like music, athleticism, what about the multiple intelligences. But, in reality, when experts in the field are talking about giftedness in children they are referring to intellectual giftedness and are usually equating it with test scores at least two standard deviations above the norm. For some reason, advanced intellectual ability has been called a gift whereas advanced physical, musical, or other abilities are called talents.
But, that being said, it should also be noted that the classic IQ tests are believed to be a bit racist or perhaps classist would be a better descriptor. There are different ways of learning about the world and it is likely that the IQ tests do not catch all children who are gifted. Poor children, children of immigrants, and children who do not speak English as a first language have difficulty gaining access to gifted programs.
It should also be noted that many school districts use a group test to ascertain giftedness. These tests are notoriously unreliable in children under the age of 8 because these kids have such a hard time sitting still and do not have as much test experience to help them. If parents can afford it, a licensed child psych. can give a battery of individual tests which will give a much clearer picture of the child's abilities. Also, special ed children can at times be highly intellectual but unable to take the regular group test. A child psych can also give a battery of tests to this child and this testing should be funded by the school district as part of the child's individualized education plan.
If you have a child who you think is gifted and you would like to find out what is available in the way of services for your child, a good place to start is your state department of education. Local school districts don't often do a lot for gifted kids but your state dept of ed will let you read the state laws on teaching gifted kids. This will help you if you need assistance getting the school district to meet your child's needs. Keep in mind, however, that most school districts do not have a lot of funds for gifted ed and giftedness is not legally a form of special ed and thus not part of special education funding.
Parents are often interested in advancing their gifted children beyond their grade level. There are pros and cons to this and they should all be weighed equally. You should consider the child's physical, mental and social development as strongly as their intellectual development. If you have a very immature, in many ways, child who is academically very bright, it may not be a good idea to skip a grade. He or she will feel the difference in age, even if they can do the work. A mixed grade class might be a better alternative, if it is available.
The most important piece of advice I give to parents of gifted kids is to pay attention to their child and let him or her follow their dreams. This is good advice for all parents but sometimes parents of gifted kids forget this in their effort to help their child excel. They may push the child into chess club or french class or 40 zillion extracurricular activities and forget that the child needs time to be a child and also time to delve deeply into favorite topics and hobbies. Gifted kids get obsessed with their favorite topics and parents can find a place in their child's world if they join in the love of that topic. Maybe the first grader knows everything there is to know about Star Wars so the parents take him the science center Star Wars exhibit. (this is my friend's child) Maybe the 4th grader is enthralled by Elizabethan history so mom and dad and child visit the library together to borrow books and movies. (this was a former student) Or maybe the 3 year old is enthralled by her yard and wants to dig and label everything and collect all the bugs and have books read to hear all day long about gardening so she can memorize the flowers and insects. (this would be my child)
Nurture your child's gifts, no matter what they are, and always remember to let your child be a child and find their way in the world on their terms.
That's the most important gift my parents gave to all of their children, who range from 'above average' to 'highly gifted' - they never batted an eye at major changes from things like Engineering to Germanic Linguistics. The only time they fell down was when my highly gifted (maybe even profoundly gifted) sister wanted to pursue modern dance. Their lack of support there affected their relationship for a while. (But not my sister's tenacity. She tried it and eventually decided of her own accord not to continue.) But I digress...
: One of the main reasons that I wasn't permitted further acceleration in school was that I was small for my age, and already younger than my classmates (I averaged around the 10th percentile; not all that shocking, considering that my mother is 5'3" and my father was about 5'6"). I'm still irritated by this particular line of thinking, it's a button for me. 
