Correct , it does not come with a charger, but only needs a micro UBS charger which most things do these days, i use my Samsung tablet lead.
IMO extra barreries are a must to extent the fun, they are relatively cheap on amazon and ebay ( £15-20 each ) and i also bought the 3 battery charging hub, again relatively cheap,( £15 max ) that also doesnt come with a charger but also uses the micro usb.It charges all 3 batteries in about an hour and a half, well worth it.
I think that after use it a few days you would like to have an external control i.e. a gamepad. In that case read about it here. For the offical tello app the gamesir t1d works great, at least in my case. Touching the screen it is very hard to know where the neutral position of joysticks is. With an external controller you have the joystick springs feedback.
Enojoy your flights! Tello is really nice for starting/training ;-)