How much luggage can i take onboard a plane?

In general:

As carry-on, one piece (with size limitations) plus a personal item such as a purse or briefcase (which must be able to fit under the seat in front of you). Know that on small regional planes, a piece that is fine as a carry-on on larger planes may have to be gate-checked as the overhead bins are too small to accommodate them.

As checked, I'm not sure there are limits, as long as you are willing to pay the fees - which get increasingly large as the number of pieces increases. For those airlines that charge, a second bag is more expensive than the first, a third more expensive than the second, etc.

Go to your airline's website for specific information on limits on quantity, weight, etc and the fees involved.

Are you talking checked baggage or carryon. Either way, each airline has their own rules as to how much you can bring and how much they will charge.

Check the airline's website and look for baggage. You'll get all the info you need right there.

Your carry-on bag and one personal piece like a purse.