What kind of classes are you looking at? For language, my friends staying in that area sed their kids to I Can Read & Berries.
For me, I dont't teach unless I find that the school is really not doing enough. I reinforce what my child learns in school only. Even then, my 1st move would usually be to call up the teacher/principal to find out how my child is doing. If I find my child lagging in some ways, I will speak to the teacher to find out the method used and do reinforcement at home using the same method to lessen confusion. There's also the Parent-Teacher sessions to ask about progress and things to look out for. These are very good opportunities to find out how and what we as parents can do to help.
To teach or reinforce, I feel the right environment must be set. No distractions, no tv, no kids playing or running around. At most, only soft soothing music. That also means both parent n child must be in the right frame of mind. No pt sitting down with the child if I had a bad day. I am just going to lose my temper with her. I also feel that if you have more than 1 sch going kid, you'll need to sit down with them separately. Give the one who is not being schooled some activites to do while you sit down with the other one.
Having said these though, I do outsource my child's learning to some enrichment providers too