I have a yamaha r125 yzf recently ran out of engine oil and burnt my engine I got new pistons and parts for my engine and I got told I have to run it in a bit as they are new parts. What do I do as some people say I have to go slow when I look on websites it says to go fast? Im not sure how to rev it or anything.

Who says go fast?
The breaking I was always told was to vary speed, and not go too fast or rev too much.
Then you change the oil after 200 miles to see how much metal is in the oil.
And of course you never ever let it go dry again... I almost did once on a 100+ degree day, but got home on the last few drops.

So can the oil run out even after one day if its full and so after 200 miles I can begin to rev again?

It's rare. I never even burned any oil at all except that one hot day.
If you want high RPMs sooner, change the oil sooner, around 100 miles. Go for a nice 100 mile highway drive going 50-55. You want to get the new metal filings out. It won't be filings so much as silvery gray grit sitting at the bottom of the oil pan. If there's a lot, change the oil again after another 500 miles. You don't want metal in your oil acting like sandpaper on moving parts.