To work on your farm you're going to need the basic set of tools. Most Harvest Moon games give these to you at the beginning, but in Rune Factory you're just borrowing a farm so you'll have to get the tools on your own.
Wateringpot - Your basic can will be given to you by Mist at the beginning of the game.
Axe - Visit Bianca when she's inside her mansion and she'll give you a free axe.
Hammer - Once you've unlocked Carmite Cave from Godwin, you'll have to till at least 50 squares of ground with your Hoe inside the cave. You don't have to grow anything if you don't want to. Once you've marked up the soil, visit Leo the blacksmith and talk to him to receive your basic hammer.
Hoe - Given to you by Mist at the very beginning of the game.
Sickle - Acquiring a sickle is similar to earning your hammer. This time you'll need to till 50 squares of soil on your own farm, then talk to Rosetta when she's inside of Jean's seed shop.
Fishing Rod - Walk to the end of the dock on the beach and Sabrina will appear to give you an old fishing pole. You must reach the end of the wooden boat dock before she'll walk up behind you, and you don't even have to introduce yourself to her beforehand.
Pet Glove - Talk to Tabatha at the mansion to receive the item you'll need to convince monsters to live on your farm. To use the glove just stand next to a beast and repeatedly press the B button until it stops attacking you.
Once you have your set of 6 basic tools (excluding the Pet Glove) you can upgrade them by going to Leo and giving him the required items for smelting, or upgrade your house to open your own blacksmith shop. The ores needed to upgrade are found inside of the caves, while the other treasures needed are dropped by the monsters you fight.
Your other set of tools will be given to you once you have befriended at least one monster to live on your farm.
Brush - Talk to Felicity when she's inside of Neuman's shop to get the brushing tool. Use it every day on your creatures to increase their Friend Points. The more FP, the more HP a monster will have. In the case of Livestock monsters, more FP nets you larger produce.
Shears - After you have at least 1 monster on your farm, talk to Camus when he's inside his shop to receive the Sheers. The tool can only be used on the Mokomoko monsters to collect their wool.
Milker - To receive the tool needed to collect milk from Buffamoo, talk to Jasper at his mansion. He'll give you the Milker for free.
Basket - Neuman will supply you with a little Basket you can use for collecting eggs from Kokehoho monsters. It is also used for retrieving Honey from Hornets and Queen Bee creatures.