How to convert a fluorescent fixture to led?
There are loads of questions with answers on this site that address this question and loads of YouTube tutorials on how to do it. 

I prefer to remove the ballast, its wiring and the tombstones.

Replace the tombstones with Non-shunted ones and wire directly to one tombstone. Use wire nuts to pigtail 18awg wire to your black and white ( line and neutral ) house wiring and wire them to the two wire inputs on the non shunted tombstone. ( ground to the metal fixtures body. )

Use a direct wire or ballast bypass led tube. 

I do not see the point in powering a ballast if it is not needed other than for people who are not comfortable making the electrical changes. ( its a waste of power )