While the process is pretty simple, it does need some preparation. You need to have access to Microrefinery and Plant bays. It is also good to build a big enough enclosed room with plant bays to secure good harvest.
After you have all that, go plant some basic fruits to the plant bays, you can use either Kepple fruit or the Gomble cactus. When all this is set up, it is time to hunt.

Get yourself a couple of nets and catch as many Chitterlings as you would like to fit in your habitat. They are a bit skittish, but can be sneaked upon from behind when they are eating.
After you have enough, go back home and release them in their new home. Throw a couple of fruits on the ground, one for each Chitterling and leave the room.
They will eat the fruits, thus becoming more friendly and every time the fruits are ripe, they gather them on their own, eat them and produce Resin.
Just be careful not to accidently kill them while releasing them, or while gathering the resin.