You can get some fruits from your island once you unlock it but other town fruits you'll have to get from people via online interactions! Unless a villager gives you a piece of foreign fruit through completion of a request but it doesn't happen all too often.
Sometimes doing favors for your villagers gets you a foreign fruit but that rarely happens. The easiest way is to make friends with other New Leaf players and either have them bring you fruit or ask if you can pick fruit in their town. Just be polite about picking other peoples fruit and leave perfect fruit alone unless they say it's alright. You can also check out the island and do tours, you can get a lot of new fruit that way!
I got other native fruit by villagers giving it to me and when I do trades I usually give some perfect fruit as a tip and maybe if they're nice they'll give you one back C:
Also, write letters to your villagers with an attached present (basically anything, maybe except for trash) and sometimes they'll send a fruit back. But most of the time, you'll get furniture, clothing or nothing.
You get some fruit from Isabelle if you talk to her before you get your mayor license thingy, and on Mothers and Fathers day you get a letter in the mail with some fruit, and you can always go to the island and other friends town to get some!