I see these jet bridges (or aerobridges) at nearly every new airport I go to. How are aircraft aligned with these bridges, particularly the A380 which has doors on both decks?
How are aircraft aligned with these bridges
They are not (but read on)
Aircraft are aligned to a point on the concrete, not to the jetbridge(s).
It is the jetbridge itself that carries out the final alignment to the aircraft door.
Jetbridges are actually motor vehicles with wheels, tyres, motors and (often) steering. It just happens that their rear end is tethered and their bodies articulate and/or telescope to accomodate the motion at the "front" end..
You drive one using a set of controls at the end furthest from the terminal building
I believe some also have what is effectively variable height suspension like old Citroens (except I imagine it is hydraulic or jack-screw).
The aircraft is driven to the terminal so the nose wheel follows a guide line and stops at a marking appropriate for the aircraft type. Then the jet bridge is driven up to the aircraft door.
As the aircraft is gradually burdened with self-loading freight and sinks on it's suspension, the jetbridge metaphorically bends its knees so that the SLF don't trip up or fall into the aircraft. That is, the jetbridge maintains alignment, the aircraft is pretty passive in the job of alignment.
I have to admit I didn't notice these jetbridge controls for many years as I was usually either busy rushing to my seat or busy rushing to the baggage reclaim. One time there was a delay at the aircraft door that was long enough for my bored gaze to alight on the controls and for the thought to briefly wander across my mind - "I wonder what would happen if I pressed that ..."
The Aircraft aligns with the gate through ground markings, radar sensors and eventually ground operators signals.
After the aircraft stops the jet bridge is aligned with the aircraft's door by an operator that commands the various bridge actuators (wheels, extension, rotation).
The bridge can move to an extent but the aircraft is driven up to a designated spot that is marked on the ground. Here is a video of it all happening.
This can be also accomplished with someone on the ground directing
They align themselves with the stand guidance system
Azimuth Guidance for Nose-In Stand (AGNIS) is a passive system which uses a system similar to PAPI lights to display red and green lights to indicate whether the plane is too far left or right.
An active system is for example the Honeywell Advanced Visual Docking Guidance. A camera detect the airplane and changes the sign to guide the pilot to the correct place.
(image source wikipedia)
After the plane is aligned to the gate the jet bridge is maneuvered up to the plane's door.