G, first of all, under current legislation across most of Europe, there is no such thing as an aerobatics rating/endorsement/whatever. Legally speaking, anyone with a PPL can hop into an aerobatics aircraft (subject to tailwheel endorsement, if applicable) and start doing loops, spins, Lomchevacks and whatnot, without any training whatsoever.
Of course whether this is wise is another matter, and this is likely going to change under EASA anyway.
AOPA has created an example syllabus which is in widespread use in the UK. You can also take the Robson book as syllabus, and there are a few more choices. But each offer a rather structured approach to learning aerobatics. Not just the figures, but also the escape routes if things don't go as planned, and the theory behind it.
After completion of such a course a school will typically issue you some sort of completion certificate. Which, as said, has no legal value whatsoever at the moment, but is nice to hang on the wall nevertheless. Plus, you will be proficient at a few basic maneuvers, such as a loop, spin, steep turns, various rolls, cuban eights and maybe reverse cuban eights, stall turns and maybe a few others.
So yes, after such a course you should be able to perform those maneuvers solo and safely in an appropriate aircraft, at a suitable height (2 mistakes high, typically).