Homeschooling is legal in all fifty United States and every provice in Canada. Each state or provice does have its own requirement and it is important to know what these are in your state. Strictly following all requirements is very important to homeschooling legally.
Some states, such as Oklahoma and Texas, have very low requirement and do not require even that notification be made to school authorities. You simply decide to homeschool and do it. (If your child has been previously enrolled in public school however, it may be wise to submit a note to the school informing them of your decision. You may otherwise wake one morning to find truancy officers on your doorstep.) Other states have very high requirements and may require teacher certification or monitoring and student testing.
The HomeSchool Legal Defence Association makes it their job to keep up on this type of information making their website on of the best places to find up-to-date and accurate information.
Whether or not it is required by your state, keeping records is not a bad idea. You never know when they might be necessary. No one plans to place their children back in public schools, but it could happen. You could become sick and unable to carry on with homeschooling. You could move from and easy to homeschool state to one in which it is difficult and decide it is no longer an option for your family. You could end up in court on truancy charges. Obtaining government assistance often requires proof of school attendance. And college, don't forget college. If there is ever a question about your child's schooling it is best to be prepared. Once you get started with a system and get into a habit it really doesn't take much time.
If you are the organized type you can probably easily work out a chart which can help you in this area. If not, there are plenty options available online to provide the help you need.