Students in the U.S. are guaranteed access to public education for elementary and secondary (high) school regardless of immigration or citizenship status.
The school district you live in will usually assign a school based on your home address. They may also have a process to apply to attend a different school in the district. Colorado law also allows a student to attend a school in a different school district at no cost and many school districts have a process for residents outside the school district to apply. See this helpful article on school choice.
You can check the enrollment process on the school district website. Here are the school districts where the downtown and Anschutz campuses are located. You can search the internet for other school districts in the area.
Child care for children who are not school age is mostly offered by private providers, although there may be a pre-school option through your school district. The City of Denver has a program for residents of Denver. See the Denver Preschool Program.
The state of Colorado licenses in-home providers and centers. You can find licensed childcare in Colorado here: https://cdec.colorado.gov/.
The U.S. government has information about the types of child care in the U.S. and how to find and choose qualify care here.
Employees who have university benefits can choose a Dependent Care Flexible Spending Account which allows you set aside money from your paycheck for dependent care. The money is not taxed and can save you 25-40% on the cost of dependent care.