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Learning starts from home. I believe the one who's always with them is responsible for whatever they've learned. Instead of forcing them to study, observe first what catches their interests. And you can use those interests to teach them. I didn't teach my 5-yr old daughter who've learned counting and alphabet just by watching CDs of nursery rhymes. I just encourage her and guide her. And correct her whenever I've heard something wrong. Now she know addition and subtraction, can spell number words, and can read fast.
Start with games, toys, or songs to impart simple concepts to babies. Explore outdoor and nature to inspire them and to spark their imagination. For programming, you can get the idea on how to teach kids basic concept on programming from here, https://studio.code.org/s/frozen/stage/1/puzzle/1. When they turn older, say 4-5 years old, you can start engaging them with these programming games. Pretty cool tool to learn the concept and logic of programming. (I learned basic programming from there too :P)
For babies, you can teach them through games. Use their toys, favourite people, food, etc to teach them basic concepts. Same can be done for science, you have to give a fun demo to get their attention and also visuals help in perceiving things in a much better and quicker way. For programming, you can actually try showing simple maths through code also. I agree you should do it in a fun casual way, don't force this learning.
It's probably important to learn the initial concepts of problem solving and viewing objects abstractly. Activities such as lego-building, understanding how nature works in the most layman terms are good examples. From there, they can explore Minecraft, and slightly older, look at Gamemaker to start building their own games. The current malaise affecting engineers now is the lack of decent problem-solving skills.
The best thing parents can do is be engaged with their children in everyday activities. Talk to them—about numbers, about the toys in the playroom—about anything at all. Take them outdoors and let them explore. One of the best practices in teaching and learning is to make learning relevant, and there is nothing more relevant than being outside and exploring the world we live in.
Not sure they can grasp complex concepts yet. So teaching them at this stage involves mostly setting the foundation for their future education. Learning should always be accompanied by entertainment. Little effort is needed since babies/toddlers are like sponges. Encouraging to use their five senses is also good. Games and music also help engage them.
I'm not really good with either but I'll try. I think you could let your child watch educational shows, and teach your child to count too (I remembered helping my younger brother count by laying out his baby snacks and teaching him 1 to 10). When he picks up a snack, I would help him to count it and make sure that he repeats it before eating it.
Read story books on math and science. Try to bring him to nature to walk around and talk about the surrounding eg. Why trees grow, leaves shape etc. For programming, if you child is above 5 years old you can sign him up for robotic learning class as a good start to learn simple programming.
The most important thing about learning, for babies and teenagers and adults alike, is for them to be able to relate the subject with real-life situations. Think mnemonic devices, dora the explorer, etc. And of course for it to be fun! The brain naturally responds well to positive things.
Start from everyday basic. Teach them math, asked them to go shop with you, count and play with the veggies and ask them to pay attention when the butcher measure the meat. The point is, make them learn and like something before you signed them to private course.