Get one from Isabelle. Once you've done a certain number of initial tasks, she'll ask if you want a net or a rod (choose the net, obviously). --- Is this finally a conundrum that CAN'T be solved by helicopter theft?
Talk to Issabel in the town hall keep choosing the top option. She will give you various suggestions for things to do. One will be bring her a shell from the beach. Do that and she will give you some fruit. Keep asking her and she will talk about filling up your encyclopedia. Talk about bug catching and you should get an option to get a net from her. Later she will give you a watering can too.
Check the Faq section there's a Faq that explains it better than I did.
You might have problems today as its the Summer soltice and she isent in the town hall.