Fracture is breakage that is not flat. The two main kinds of fracture are conchoidal (shell-shaped, as in quartz) and uneven. Metallic minerals may have a hackly (jagged) fracture. A mineral may have good cleavage in one or two directions but fracture in another direction.
To determine cleavage and fracture, you'll need a rock hammer and a safe place to use it on minerals. A magnifier is also handy, but not required. Carefully break the mineral and observe the shapes and angles of the pieces. It may break in sheets (one cleavage), splinters or prisms (two cleavages), cubes or rhombs (three cleavages) or something else.