Manual piloting
Manual piloting requires double clicking in empty space. Your ship will then head off in that direction. How far zoomed your camera is affects your perspective. So if you require precision, zoom out as far as you can. A simple example of manual piloting is when your ship is stuck on a collidable structures. If you can't align to warp because you're too close to the structure, you have to double click away from it to increase distance. An even simpler example is changing your ship's speed.
Slingshot Maneuver
Used for: breaking target's orbit
Relies on: agility
Fly in a straight line until target is heading in the same direction as you are eg. if target is orbiting clockwise from top view, this would be directly to your left (9 o'clock)
Do a 180 degree turn by turning camera to see the front of your ship and double clicking behind you (6 o'clock)
Eve Opportunist Slingshot link
Eve Opportunist Anti-Slingshot link
It should be noted that during step 4 you can either escape from the villain's point range, OR try and burn straight at him once he has reached the zenith of his orbit, and then attempt to land tackle.
Spiral Maneuver
Used for: closing distance to target while keeping some transversal velocity (not applicable to incoming missile fire)
Relies on: max speed
Move camera so target is in center in front of you (12 o'clock). Double-click halfway between center and edge of screen. Continue to double-click as you get closer. Note: the further away from the center you double-click, the more transversal you'll have; however, it will take longer to reach the target.
Counter: one way to counter a spiral is move to where the spiraler is going. If the spiraler is headed x/y (where y is towards you and x is perpendicular), then also move x to cancel transversal. ie. it's easier to shoot a moving car if you're going beside it at the same speed instead of turning your gun to follow it
The Altruist Tracking and Spiral link
Kiting
Used for: keeping target at range
Relies on: max speed
Move camera so target is in center behind you (6 o'clock). Double-click in that direction so you move away from target.
Counter: One way to counter kiting is to further increase distance. If you're chasing, turn around and have the target chase you (the target would like to keep within optimum range). When this happens turn back towards the target at full speed (an ab/mwd would help here). The target still needs time to turn around and accelerate. Hopefully you can get within your range while this happens.
Pre-aligning Acceleration Gate
Used for: instant activation of acceleration gate
Relies on: camera zoom/speed control
Unlike stations, stargates or celestials, you can't align to an acceleration gate's destination. Zoom out and line up the camera so the acceleration gate is straight on your sights (the large end of the acceleration gate should be directly behind the small end). Double-click along this direction (you can't double-click the gate itself) so your ship is pointing to where you'd accelerate to.
Alternative: activate the acceleration gate and cancel warp (ctrl+space by default) before your speed reaches 75%. Then quickly click on the right of your speed indicator to enable full/75% speed.
In either case, set your speed above 75%.
Bumping
Used for: prevent target from aligning
Relies on: mass, speed, ab/mwd, timing, range
Approach target. Activate afterburner/microwarp drive. Bump. Note: microwarp drive bumps more than afterburner. Ideally, you want to have enough range to reach maximum speed and not run out of cap for your ab/mwd
Yelling "RAMMING SPEED!" is acceptable during non-combat situations. Ask your fleet if you're unsure.
Skills
Agility:
Evasive Maneuvering: 5% bonus to agility per level
Spaceship Command: 2% bonus to agility per level
Advanced Spaceship Command 5% bonus to agility per level (only applicable to ships requiring skill)
Max Speed:
Navigation: 5% faster sub-warp speed per level
Modules
Agility:
Inertial Stabilizer (passive low-slot) (penalty: increases signature radius) (low pg/cpu use)
Max Speed:
Afterburner (active med-slot) (penalty: increases ship mass/agility when active) (med/high pg/cup use)
Microwarp Drive (active med-slot) (penalty: increases ship mass/agility when active and reduces capacitor capacity) (high pg/cup use)
Overdrive Injector (passive low-slot) (penalty: reduces cargo capacity) (low pg/cpu use)
Both:
Nanofiber Structure (passive low-slot) (penalty: reduces structure hp) (low pg/cpu use)
Rigs
Agility:
Low Friction Nozzle Joints (penalty: reduces armor hp)
Max Speed:
Auxiliary Thruster (penalty: reduces armor hp)
Both:
Polycarbon Engine Housing (penalty: reduces armor hp)
Big Slow ship MWD 10 second warp
MWD Cloak Trick
see Cloak Trick