I wasn't around in 1500,
but I sure am around now.
I existed 30 years ago,
but to use me, people would say “How?”.
30 years ago, phones existed but were more old-fashioned and worked differently. "How?" might also be a humourous reference to tribal greetings, basically people say "Hi" to use a phone.
I come in two main forms,
one portable; one not.
Mobile phones and landline phones.
I'm very costly,
so you shouldn't throw me in a boiling pot.
Phones nowadays can cost hundreds of pounds.
You can use me for work,
or for play.
You can do work (emails etc.) on a smartphone, or use it to play games or do pointless nonsense.
Or you can use me
for a school research day.
I suppose so.
I am fairly small,
but I used to have a much bigger size.
Mobile phones nowadays are small, but they used to be much bigger decades ago.
Now when you guess what I am,
please don't tell me lies!
These lines are probably just decorative and not meant to be clues in themselves?