We're on the autonomous end of the spectrum, so we do whatever the kids want to do. When they are young, for most children that usually means playing. Among other things, today my 6yo played in the bath, played with dolls, played a logic game on the computer, watched science documentaries, played at the neighbours' house, pestered me into making cupcakes with her, invented a gadget for changing dolly nappies, drew, went to the local shop, worked on a scrapbook (inspired by Paddington Bear's habit) and wrestled with her teenaged sister in bed.
My 13yo spent much of the day drawing geometric shapes while listening to a Harry Potter audiobook. She also played guitar a bit, chatted with a friend on Skype, took her little sister for a walk, got me to show her the basic idea of trigonometry, helped dad fix the car, posted on an online forum for people who draw cartoons, asked about the causes of the American revolution and then watched a TV drama and a documentary which were both related to that subject. (When I started to write this paragraph I was going to say all she did was listen to the audiobook and draw. You don't always notice all the other stuff unless you sit down to list it! It just happens...)
It's rarely me who thinks up projects, though if I hear of a good place to go or a museum event etc then I might initiate something. In our house, setting the agenda is the kids' job.
Confident? Yes. Initially that came from reassuring myself that since some countries only start formal education around the age of seven and their kids do well, there was no need to stress until my dd was older than that. Then my confidence increased through seeing so many older home educated kids who were thriving in all their beautifully diverse ways. Finally it was cemented by noticing how much my own children had learned already.