The company is called Tesco, so saying, "I went to Tesco's" - meaning I went to the shop belonging to the company of that name - is correct.
However, and it's a big 'however', most large businesses stopped using the apostrophe in their names some time ago.
For example, no one who works for the bank ever writes "Barclay's bank" but only ever "Barclays bank". Similarly, the chemist founded by Jesse Boot is called "Boots", not "Boot's". Consequently, there is not much wrong with writing Tescos with no apostrophe either.
So, I went to Tesco, Tesco's or Tescos are all acceptable, depending on how you yourself see the situation.