I have to admit that I would not have chosen to do this myself, but this was very important to my husband and so I added it onto our morning Bible time. After we read the Bible and pray, I go right into asking the questions.
Catechizing sounded hard to me, and I wasn't sure how to start- none of my friends were doing this (to my knowledge), so I just started out reading the questions and the answers, one at a time, to our kids. I use a sing-song kind of voice to help them learn.
Each day I start back with the first question and add additional questions when it seems they have the gist of the previous questions. (When we got to a certain point with our oldest I would just review the first questions every week or so.) We spend at the most five minutes a day on this. It just doesn't take long for young children to memorize vast amounts of information.
I was surprised last week to realize that Sophie (age 3) knew almost every question Josh (age 5) knows. I haven't worked with her past the first five questions or so, but she is present for Josh and Carter's questions, and has learned them just by being around.
No need to wait until the kids can understand what they are learning. This is memorization tool that serves to build theology into their little minds while they can memorize anything you put before them. I'm sure we all have songs we memorized as children before we understood the words and now as adults we are a bit shocked (ok, ashamed) that we knew the lyrics to "Like a Virgin" memorized way before we knew what we were singing along to. Even if you didn't know that particular song, you know what I am talking about.
We have been shocked at how much theology our kids have learned this way. The catechism gives them a framework in which to view the lense of Scripture. I do not believe this knowledge saves them or changes their hearts- only God's Spirit can do that and we beg God for the salvation of our children. But it is our prayer that God will use this knowledge like a well of water that they will draw from for the rest of their lives.
Still dubious to the benefits of catechizing your children? Here is an article (from a presbyterian perspective) you may find helpful.