An apostille is a stamp and a small piece of paper that is attached to the back of your document that certifies who I am to other countries, and that my signature and seal are genuine. It can also be attached directly to documents that typically have a wet or ink signature issued by a government body. They are issued by the Foreign, Commonwealth and Development Office in Milton Keynes. You can request that they do this for you directly and have a handy document checking tool on their website that will tell you what documents they will accept and whether or not it needs to be authenticated first.
Legalisation is in addition to this. In this case an embassy or consulate of the destination country and will confirm the apostille. Each embassy is different in what they require and their fees. I typically use a reliable and discreet consular service agent to obtain what you need, and all costs and fees will be provided to you in advance.
Whether or not you need an apostille or both will depend on which country you want to use your document(s) in. In some countries the notarised document is enough, typically commonwealth countries, in others you need an apostille and some require legalisation. Whoever has prepared or requested the document from you, will be able to tell you what they need.
If this is something that you need assistance with, please do not hesitate to contact me.