You can acquire the various silver tools by satisfying certain requirements, as indicated below.

Shovel - Donate 15 fossils to the Museum, then buy it for 500 bells when it randomly appears on sale on the building's second floor.
Fishing Rod - Donate 30 fish or sea creatures to the Museum, then buy it for 500 bells on the building's second floor.
Net - Donate 30 bugs to the Museum, then buy it for 500 bells on the building's second floor.
Watering Can - Purchase 50 or more flower seeds.
Axe - Randomly available on the island, in exchange for 8 medals.
Slingshot - Shoot down 16 presents, then shoot down the slingshot (held aloft by two silver balloons)