Catching bugs is another way of earning quick bells since most of them can be sold at a really good price. To be able to capture bugs, you have to get a Net first. You can buy one from the Nookling Junction or get it from Elizabeth as one of the options in getting advice on how to live the town. (This option is only available when you just moved into town) The ordinary net can be later upgraded to a Silver and Gold net. Refer to this guide’s “Tools” section for more details.
Bugs usually hang out on tree trunks and stumps. You can catch other flying bugs such as butteflies, dragonflies, bees, etc. Other certain bugs are also found on the river or after hitting a rock. Certain bugs, especially beetles are quite sensitive and will fly away if you run near them.
Tip: For new types of bugs you catch, it will be a good idea to donate them to the Museum first so you can just sell any succeeding bugs you catch of the same type.
After finding the bug you want to capture, equip the net then press and hold “A”. This will make allow your character to ready the net. Once you’re in range, release A to swing the net downward. This is a very helpful technique when you’re sneaking behind a beetle.
I'm pretty sure it's Isabelle and not Elizabeth.