How do I get more honey, nets, etc?

Not yet, at least. There aren't any in-game mechanics for getting more vanilla nets/honey.

You can now get additional nets, honey and fertilisers in the following situations

• Completing goals in fishing tourneys and gardening events
• Popping yellow balloons that occasionally show up on the map (I think higher friendship levels may increase the chances of this?)
• Occasionally as a reward for opening the game daily