Sarah,
Are you in the U.S.A? If so, homeschool laws vary by state.
For instance, in my state (Missouri), homeschoolers are not required to register. We have to provide the equivalent of 1,000 hours of instruction, 600 of which must be in the core subjects. We need to keep some records of attendance and samples and/or evaluations of each student’s work. A daily log is generally the easiest record to keep.
You can find your state laws by doing an internet search, or sometimes they are available on your state’s government website. If you register on the HSLDA website, or become a member, they also provide that information specific to your state. In some states, it is highly recommended by veteran homeschoolers that you become a member of the HSLDA; in others, it’s not as necessary, but may still be a good idea.
If you are in another country, you might still be able to find something out about your local homeschooling laws by searching online, or perhaps the HSLDA or another homeschooling-related group can provide information.
Many curriculum providers allow copying of their materials for at-home use; some do not. I generally try to buy the ones that do allow it, so that I can reuse the materials for younger siblings. Some companies have “consumable workbooks” that are separate from the textbook, so that I only have to buy one textbook for all the kids, and then simply purchase a new workbook for each student that I expect to use it.
If there is a homeschooling group in your area, I highly recommend checking it out and joining (particularly if it’s a Catholic group). The other homeschooling parents will be able to help you find answers specific to your state/area, point you to available resources that you might not otherwise know about, and/or provide a social outlet for you and your kids.
HTH! God bless!