If you’re going to trade under your own name, you won’t need any business registration. However, if you want to trade under any other name you’ll need to register a business name.
You only need an AFSL if you are providing a financial service or a financial product. Generally training people is neither of those.
If you’re going to deliver Nationally Recognised Training (e.g a recognised course with a Unit of Competency, Certificate, Diploma, etc outcome), then you will either need to become a Registered Training Organisation with the relevant qualifications on scope, or have a third party arrangement with an RTO that does. To generally train and assess Nationally Recognised Training you must have a training and assessment qualification (‘TAE’) to at least Certificate IV level (or higher) and the qualification you’ll be delivering (or higher). So, if you want to deliver a Diploma of Business for example, you’d need TAE and a Diploma of Business or higher. If you only had a Certificate IV in Business, you couldn’t deliver the Diploma.
If you’re not going to provide Nationally Recognised Training (i.e. no qualification outcome) you don’t need any registrations or licences to do so, but you must be careful not to give any impression that the course will have any type of qualification outcome or equivalency.