Required Material
When you get to "Chapter 2" of the story line, walk around the jungle and you'll eventually come across many vines. Some vines are on the ground and others are hanging from the trees. Tap a vine with your stylus to pick it up. You only need one vine to make a rope, but pick up several vines to keep in your inventory for later use.
Making the Rope
Take the vine to Claire. When she asks what you want to talk about, select "vines" from the pop-up menu. She will take the vines from you and put them in the corner. Go up to the vines, tap them and ask Claire to make a rope for you in two days. When two game days have passed, talk to Claire again. She will tell you the rope is finished and is in your inventory.
Rope as Key Material
Rope is needed to craft many things. It can be used to build a bridge, a small raft, a wooden house, a large raft and furniture for your home.
Considerations
If your inventory is too full for another vine, go back home, press the "Y" button and then "A" to talk with Claire. Tell her you have something to give her and then say "Please hold on to this." Give her some of the items in your inventory to free space for the vines.