Your tools in Stardew Valley is something that you are going to be using a lot, and it's definitely worth upgrading them. You start of with a regular Hoe, Pickaxe, Axe, and Watering Can, and all four of these can be upgraded to cost less energy, perform better, and do new stuff such as cutting down logs or shattering huge rocks.
There are 4 upgrades for all four tools; Copper, Steel, Gold, and Iridium. In order to upgrade your tools, you need to head to Clint the Blacksmith and select the option "Upgrade tools", while also having the tool in your inventory.
The cost for upgrading your tools is as follows:
Copper upgrade: 5 Copper Bars + 2,000g.
Steel upgrade:5 Iron Bars + 5,000g.
Gold upgrade: 5 Gold Bars + 10,000g.
Iridium upgrade: 5 Iridium Bars + 25,000g.
Once you purchase an upgrade from Clint the Blacksmith, it will take him the next three days to finish the upgrade. This means that you should plan carefully ahead in order to prevent your crops from dying when you are upgrading your Watering Can.
After three days has passed, return to Clint to pick up your upgraded tool.