A Bucket of sap is obtained by using a knife with an evergreen tree, while having a empty bucket in the inventory. You cannot get sap from a maple tree. A knife within the toolbelt will work; just use the empty bucket on the tree. One place to find evergreen trees is just north of the Falador lodestone.
While many quests guides claim you must get sap from an evergreen, there are also many trees which give sap that are not described as 'Evergreen'. Usually they appear slightly taller and pointier than those surrounding them. A useful bunch of these trees may be found north of Falador. The examine for these trees is: "A commonly found tree." instead of "One of the most common trees in RuneScape."