What do the slot shapes mean?
Diamond = battery hardpoint, triangle = subsystem, circle = propulsion.
- Diamond: turrets, missile and torpedo launchers, dronelinks, mining lasers and repair projectors, e.g.
Auto-Cannon, 
Mining Laser, 
Repair Projector. You can't fit more battery modules than the hull has battery hardpoints, so a mining laser or launcher takes a turret's place. - Triangle: ECM and other modules you switch on yourself, e.g.
Thrust Scrambler, 
Tracking Disruptor, 
Defense Shredder, 
Armor Hardener, 
Target Painter. - Circle: propulsion modules, e.g.
Impulse Nacelle. - Core slots have no symbol and take any module that doesn't need a hardpoint, plus conduits. Core modules can also sit on hardpoints.
- Shaped modules only need to cover one matching hardpoint; the rest can lie on any free cells.
Tip
Press R while dragging a module to rotate it.
Changed in Beta Patch 2: missiles and torpedoes used to go on subsystem hardpoints (triangle).