Home education is done on much much smaller scale; you're only doing this for a small number of children at a time and you can literally observe them and converse with them at the time. It's a lot more immediate than in a school setting. And you're adapting and correcting as you go along. There's no need to formally assess in the same way that a teacher would have to do.
If you realise that your child already "gets" something, then you move on to the next thing, there's no requirement to do ten more exercises (for example) on the same thing. Equally, if your child isn't getting something, you can slow down or try something else without having to worry that 29 other children are going to be held up or you that aren't going to get through your week's/term's curriculum.
For the rest, I can only speak for myself because every home educating family does things a bit differently:
I was not spending a lot of time lesson planning. I used to have a loose plan of what they should be able to do for English and Maths each year. For other subjects, it was more like: we'll do ancient history, biology and physical geography this year, which I would "pitch" at the level of the eldest and "explain downwards" if the younger ones didn't understand.
Since we only ever did "formal" stuff for half a day, the other half a day they were free to play or explore whatever they wanted, assuming we were at home.
I did not spend any time increasing my own knowledge in advance. Whatever I didn't know, we'd look up on the spot. (Obviously this would be unworkable in a classroom). If they wanted to know more, then we'd just keep on looking things up.
For the activities and trips - Some of these would "pop out" from the reading aloud or I would generally have something vaguely in mind and I would google for more specifics or to firm things up.
I did not "set up" activities in advance - they would have to help set up anything with me (again, probably completely unworkable in a classroom).
Also, the trips took a lot less planning than a school trip would, as, apart from may be inviting other families to join us, we could just get in the car and drive there.
My "teaching" was nowhere near perfect (and definitely not as polished as a school teacher's delivery) but it kind of didn't need to be because they could ask whatever they liked, whenever they liked and I also knew that we'd cycle through the history timeline two or three times over the years, so each cycle would also reinforce the previous knowledge.
Compared to school pupils, there are some things mine knew in more depth such as world history because it's not a focus in the national curriculum and other things, like fronted adverbials, that they were completely oblivious of.
I did not worry about this in the slightest - although I realise that this sounds somewhat alarming.
I think mostly, what I was trying to do was show my children that anything that they didn't know they could look up and learn and it would be fine.
(Edit: sorry that was so long!)