My DCs school is good at sending home notes telling us what they have done this week and will do this half term etc. So you would know there was a big thing going on about penguins, for example, and you could do your own penguin related activity too.
DS1 is not very good at telling me what goes on at school, but DS2 chatters away. I tend to find out what is happening in DS1's class from speaking to the other mums. It is worth investing some time making friends with other mums, IME, they can be a great support network.
I agree with others you should get some feedback from your childcarer as well - my nannies have kept me in touch with school.
We do reading practice at breakfast time, because they are too tired at night. DS2 is in reception and does not get homework apart from reading. DS1 does his homework with his nanny and sometimes with us at weekends if they have had a busy week.
If the school gives us enough notice about things, I try to work at home that day and show up. There are special reading assemblies sometimes, quite often opportunities to hang around for half an hour before other people's children read out more fluently than your own little darling can manage, all at short notice naturally. However the DCs place great importance on a parent being there and you can catch up with the other mums. I also keep a couple of days holiday in reserve for going on school trips.
I do drop off about once a week.