You see akshay tritiya is seen as day of creation when Lord Bramha Started creating the srishti (universe). There are four more aspects related to it.
Parshurama Avatar Janma(Birth of Lord Parshurama).
The (never-ending/Akshaya) Svyam Siddha muhurata also known as Akshaya muhurata.
The (not so very famous) Lord Vishnu's Haygriva avatar also appeared on Akshaya tritiya.
The Mahabharata Literature writing (by Lord Ganesha) and dictation (by Lord Vyasa)started on this day.
So coming to the point of celebrations it is done at personal level (that is what people want in akshaya(never ending or endless) amount). In temple's though they celebrate by giving Lord Narayana a mango Bath or
"amra-abhishek" and a full fledged fruit abhishek to Lord Rudra/Shiva in Shiva Linga form.The fruits which are freshly arrived in the season are first offered to God before consumption that is why abhishek with fruits is done.
Talking about celebrations out of India it is the individual choice of the people, they can celebrate by making fasts and buying precious things (as they like or majority of them do) for the wealth or prosperity to be akshaya(never ending or infinite). But there are no large scale celebrations like Diwali and Dusshera outside or in India. Only worship and Pooja (in various forms like Fruit Abhishek) is done.
For refrence see this