How can I prep and paint a child’s table and chairs?

You need to sand the wood down using sandpaper. If it is already quite smooth you just need a light sand to give the new paint a key to fix to. If it is quite rough then you will need to sand it until it has a good surface. Clean it down with a damp cloth and then decide if it need undercoating or not. If it is dark in colour and you are painting it a light colour then undercoat. If is already a light colour then you can paint directly onto it. If it is not perfect after one coat, wait for it to dry and then re- coat it.

Your end product depends on the prep!!!!!! It depends on how great you want it to look in the end and if you want it to look GREAT ...believe me the PREP IS EVERYTHING.... it matters!!!! But definitely consider if this is a piece that you will want keep for a long time and only go this route if you want to keep them for a while! The reason I say this is because this method will take a lot of your time and is tedious but will look like a professional finish job if you do it well.:

To go all in to get a GREAT result, that means, prepping by SANDING, PRIMING(maybe KILZ or B Moore primer) and using steel wool between coats of primer(to get that super smooth finish) all BEFORE you paint. Start with a 180 grit and move up to 220 when you are sanding. ALSO...the paints are a huge factor. With a kids table with a lot of traffic you will want to use something super heavy duty! Consider using a home paint sprayer for the job to get that super sleek pro finish. If you are putting the time in to prep well and paint them well you will want a good paint that will last. Benjamin Moore ADVANCE!! $50 per gallon but it's so worth it!!! Use it in the sprayer or brush it on if you don't have one. That paint is an excellent cabinet paint and you don't need a topcoat. I seriously just wipe it down when it gets dirty.

If you want to just change the color for a few years then there are definitely easier methods to paint them. IE: spray paint. I just wanted to give you a lasting solution in case you didn't want to deal with chipping, brush marks and lots of wear in a short few years using other methods. B Moore advance paints really last!!! I use it all of the time. You can see the finish in this dresser that I redid with that paint....

https://karupp-did.net/fetor-to-fetching/

Good luck!

I would do primary colors

One chair one blue and so on.you could also name the chairs by their color .a learning tool as well a table and chairs

Scuff with either sandpaper or fine steelwool. Clean with denatured alcohol. Then prime and paint. If you are good with a sprayer (not dripping) that renders the most professional results.

Lightly sand to remove an gloss with 220 grit sandpaper. Prime with Kilz Primer. Then paint your color. Seal with at three coats of a water based polyurethane to protect the finish.