"West Ham United were probably playing at their best when they managed to beat Liverpool home and away this season." (my own example) "When summer weather is at its finest, it's natural to want to avoid the kitchen." (from http://fraze.it/n_search.jsp?q=at+finest&l=0)

These are the same, but don't use an apostrophe. At its best or at its finest.

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.