Ask HN: Investing money for your children

If you're in the U.S., you should learn about tax-advantaged educational savings accounts, such as Coverdell accounts:

https://www.irs.gov/taxtopics/tc310.html

If you're completely new to investing in general, you should learn about basic issues of investing, such as the impact of fees on the long-term returns of investments. For example, directly opening a mutual fund account with a low-cost provider like Vanguard is usually a much better deal than going through the sales people at your local bank (who will gouge you on fees).