Since it’s a new harp, you can always check with the manufacturer.
I don’t know if there’s one right method, but you always want to tune with your pedals in flat position. Some like to tune all the Cb’s, the Gb’s, Db’s, etc. Some just go from middle Cb stepwise on up and then from middle Cb on down.
How to “season” a harp has as many opinions as there are harpists. I would recommend always playing with good tone over all the octaves, i.e. arpeggios and chords. Keep the harp in a room with the correct humidity. And maintain your harp in good working order – keep it in tune, out of direct sunlight and big jumps in temperature and humidity.