Firstly, it's important to note that you can never use this 'properly' if the punctuation is wrong. As 'its' is a possessive - rather than a contraction of 'it has' or 'it is' - there should be no apostrophe.
The expressions 'at its finest' and 'at its best' can be used like this:
'Da Marco' is a superb restaurant - regional Italian cooking at its best.'
This means that the restaurant is an example of what regional Italian cooking is like when it is done to a first class standard.