First:  Homeschool.

Second:  Make sure your homeschool includes good catechisms and religion is fully integrated into every single subject.  

Third:  Don't worry too much about "paying attention" for the rosary, it will come; but call out children who do not participate.  Repeat prayers as needed.  Saying the prayers is the foundation of the rosary just as memorizing catechism questions is the foundation of knowing the religion.

Fourth:  And I say this from personal experience:  As long as the child goes to the Novus Ordo, getting kids to become devout Catholics is virtually impossible.  I've known a precious few who have successfully raised faithful Catholics in the Novus Ordo, but they are very few in number and there is still the inherent possibility of falling away into one of the many heresies so prevalent throughout conciliarism.  The Novus Ordo simply does not reinforce the catechism (and is often outright contradictory) and the service is simply too boring for children (it doesn't do much for adults either).  

A note on this last item:  Back in my Novus Ordo days I was on the parish council.  A discussion arose about why Confirmation is not administered until children are 17 years old.  Ultimately, the answer was that this was the only way the parish could keep kids in the "Religious Education Program" through high school.  One man agreed that this was a real good idea because, after all, everyone knows that the children will fall away from the faith after they graduate but, if they had all that extra Sunday school, they would eventually realize that they need to return the the Church, especially when they have kids of their own.  It was only after I escaped the Novus Ordo that I learned that Confirmation should be administered before children enter adolescence since that is when the temptations are going to be greatest.

This is my advice.  

It's a difficult question because the "best way" depends a lot on the child -- their interests, temperment, etc.

As mentioned, setting a good example and praying for him/her are very important.

The more he/she is immersed in the world -- TV, movies, music, sports (viewing, not playing) -- the more difficult it will be for them to develop any sort of appreciation for spiritual things.

I'd recommend a few age-appropriate books, but so many children these days would never open a book they weren't required to read for school.

If he/she has any "normal" interests (nature, history, music, ...) there could be an opportunity to interject elements of the Faith into discussions or activities. On the other hand, if their only interest is in the latest movies, you won't find much opportunity for this.

Especially for younger children, participating in the family rosary is more about building a habit and setting an example than about focusing on the prayers. But, it might help school-aged children to stay attentive by providing pictures to go along with the mysteries or by taking a bit of time to explain each mystery before it is prayed. Of course, this can be helpful at any age, but I find my preschoolers will say the Rosary with us just so they can stay up a few extra minutes and not have to go to bed. : )

Example is a big one.

They need to know and love someone who not only says all the right things (which we're all experts at), but really lives them, especially when it causes suffering that the children can actually see. Not that adults should put all their suffering on display, but there are bound to be occasions when the children see the adults put it uncomfortable situations and it is crucial that the children see the adults handling them with all humility and charity. They have to have occasions in their memory to draw strength from when it's their turn to make those choices.

Along the same lines, the saints HAVE to be their heros. Tell them story after story after story of the heroism of the saints. Inspire them to magnanimity. Show them how to achieve that magnanimity in the little things. Children are very naturally selfless and loving and put adults to shame when given the chance. Develop those virtues while they are still moldable. For example, if two children are fighting over one toy and that toy belongs to one child, encourage that child to share. Set a timer so that the other can play with it for 10 minutes and give it back, but definitely encourage difficult, selfless acts while they are young. (Then you have to watch and make sure the other child doesn't take advantage, knowing that's what you'll encourage, lol, but it's still a good exercise if you keep your eyes open.)

Also explain the Faith. Make sure they understand the why's, no matter the age group. Everything can be explained age-appropriately. We tend to think that because Faith means believing without seeing then we shouldn't have to understand, but that's not true. We should spend less time telling and more time explaining. Make sure they understand how it all makes sense in so far as they can. When the grace of Faith is dim, a trial we all undergo to varying degrees, they will NEED to have reason to fall back on. It's the safety net when we fall so it has to be sturdy and well-built if we hope to survive.

Just as I hit submit on the last post, it occurred to me t hat my kids grew up almost completely without TV.  I expect that helped a lot.

Well, okay.  I am never one to turn down a compliment.

I know of other parents who did what we did, with very different results.  

I think the fact that my wife and I took such positive joy in our faith, and made that joy a palpable part of our family life (according to my children), made a great difference.  We did not hide the fact that living by our faith is hard, and not always fun in a worldly sense.  However, We also seem to have led our children to understand that it is the greatest joy one can have in life, and that this joy more than outweighs the hardship.

I remember reading a book in which a rural Pentecostal minister was quoted as saying something like, "Following Jesus and living according to His teachings would be the greatest, happiest, most blessed way to spend a life even if it were only for this world, even if there were no life in Heaven."  How wonderful it is that it is NOT just for this world.

My own experience:

Stop going to NO Mass if possible.  We left last year and have not returned.

Homeschool if possible.  All of our curriculum is rooted in Catholicism.  When everything the children learn has God as the center, many things come much easier.

The Baltimore Catechism.  Our 10 year-old has done extremely well with this format of questions and answers and learning by rote.  Our 16 y/o declared last week that he wished he had learned this because he has missed so much.  I wished I had known about it when I converted.

Continue to pray together.  We have Morning Prayers, Meal Prayers, Rosary, and Evening Prayers.  Children learn really quickly and they are proud of what they learn.  It didn't take long for our children to learn their prayers.

Interesting books about Catholicism and the saints.  Find things they are interested in and use that as a spring board.  This year, our son read about St. Augustine, St. Jean Baptiste Vianney, and St. Damien of Molokai.  

Fill your home with signs and symbols and sacred objects.  You will be surprised these days where you can find them.  I found a beautiful painting of the Sacred Heart of Jesus at a garage sale.  I also found some inexpensive fleurs-de-lis.  Show them Catholicism.

Don't forget to pray, often.