Just bought a car at a dealership. It is used and have 42k miles on it. How do I know when I should start to do routine maintenance?

Pull the dipstick and look at the oil. If it looks clear and clean then change it in around 3,000 more miles. If it looks dirty change it now. After that follow the maintenance schedule as listed in your owners manual. BTW, if this is a newer model car it may have an oil change maintenance minder that will tell you when to change the oil.

Did the dealership not provide a history of the vehicle? As in did they provide all of it's service and maintenance receipts? If not, there is no way to know what the previously owner may have or many have not performed. If that is the case can almost presume everything which is mentioned on the scheduled routine maintenance list is needed.

Just follow the maintenence schedule in the book. If your oil looks black have it changed. When changing the oil always change the filter too

Changing your oil now would not be a bad idea, it won't hurt the engine to change it, even if it was only done 100 miles ago, this way you know what cycle it is on. You should basically assume the vehicle is new (to you) and start at 0 on things like Oil Change, Tire Rotation etc. Things that are more involved (Timing belt, tune ups, spark plugs, etc, Do those as recommended in the book (45K, 60K, etc...).

Have it done now and if you already have a decent relationship with a decent mechanic, have also give it a once over.

I'd change the motor oil right now and then change it every 3,000 miles unless you use synthetic oil in which case change it every 5,000 miles. Change the transmission fluid every 60,000 miles.

If you bought it from a new car dealer they probably did a recent service. Ask them!!!!

Changing the oil would be the minimum that the dealer should have done. Go back an ask what, if anything, they did in terms of maintenance to prepare the vehicle for sale.
Anything they did you can consider as part of the routine maintenance schedule. For everything else, replace parts in line with the manuals suggestion, unless there are obvious signs of premature wear or failure.
As for you changing the oil, good for you. It won't hurt to change the oil 'prematurely'. In fact, it is the number one thing you can do to prevent premature wear and break down.

The dealership will have a record of work they have done on the car. So phone and ask them. If you get no satisfaction assume nothing has been done and start the routine,.