Introduction
The first thing you'll notice about movement is the fact that Dreadnought implemented inertia and impulse physics.
For those coming from GSF or comparable space shooters this is a big difference.
There is no instantaneous change of direction. You always should think some seconds in advance for navigating around obstacles or for flying on a good attack vector.

Fortunately, you don't take damage from collisions with obstacles. Though your speed and direction will change depending on impulse and collision angles.

As another core characteristic the ships stay oriented to the horizon. You can ascend and descend. And nose or aft may point slightly downwards or upwards when ascending or descending. But there is no free 3-D movement in terms of having your ship face any direction on the vertical axis.
Even the fastest ships can't dive down or fly loops - which is kind of odd to me but will most likely have some balancing reason.
But as a result, most players won't have serious issues orientating themselves on the maps. As a side note: in GSF I always found those being able to ignore the horizon were at an advantage.

Besides those distinctive features Dreadnought of course allows you to accelerate, decelerate, turn, ascend, descend as well as temporarily boosting movement characteristics and flying maneuvers.

Obvious as soon as you play, but to make this introduction complete: your view is disconnected from the direction your ship moves. So, mouse movement doesn't affect your ship movement. Which is definitely required with all those 360° firing arc weapons around.

Basic Controls
Dreadnought features WASD movement with [W] and [ S] for moving forward and backward and [A] and [D] for turning. There is no strafing.
In addition, you can ascend with [Space] and descend with [ Left shift].
Keys have to be pressed and held to move continuously in the chosen direction.
Your mouse movement does not affect your ship movement.

Since Dreadnought implements inertia and impulse and uses thrust power values and maximum speeds you will notice that it takes a notable amount of time to be at maximum speed.

Warning: You will find yourself often wanting to use three of those movement keys at once. Your keyboard might interfere at this point! Many keyboards only support 2-3 keys being pressed at the same time. Additional key inputs will get lost. So, depending on the order you pressed the keys either a movement direction or - what's usually more annoying - activating ship modules won't work!
If you experience such issues, try to stop pressing the movement keys for quickly activating a module and then continue using the movement keys.

Maneuverability
There is a maneuverability rating on the tooltips and ship descriptions in the tech trees.
As it is a combined rating you may treat this as a rough approximation to speed and handling.

Two ships having the same rating doesn't mean they fly the same.
For example, heavy artillery cruisers (Jupiter Arms) are labeled with 29. That's close to medium dreadnoughts (Akula Vektor) which have 33.
While that dreadnought is about twice as fast as the artillery cruiser, the cruiser turns more than twice as fast as the dreadnought (without taking boosting into account! (see below)).

But in general, you can expect ships of the same class but of different subclass (light, medium, heavy) to behave similar in terms of general handling.

Corvettes are usually the fastest and most maneuverable ships, while dreadnoughts have stats at the lower end of the scale - especially for turning.
Artillery cruisers and tactical cruisers tend to have slow to medium base speeds but turn quite good.
Destroyers usually have medium to medium-fast base speeds and medium turning ability.

Boosting
All ships come with a self-replenishing energy reservoir. This energy can be used to temporarily boost speed and maneuverability by pressing [F1] (or [F3] if bound in GSF style).
You don't have to hold the key, you just have to activate this "Power to Engines" (PtE) mode.
Deactivating energy usage is done by pressing [F4].

Energy consumption is about the same amount per second on every ship regardless of speed, ship mass or other characteristics.
You usually don't want to drain your energy completely as you may want to have some energy left for shields or other purposes.

Expect your ship's speed and maneuverability to at least be doubled.
But boosting doesn't affect all ships in the same way.
It even doesn't affect all thrust directions in the same way.

While forward thrusters are usually affected the most, steering usually is least affected.
There are also dramatic differences in how ascending and descending is boosted.

Boosting Effects by Class and Manufacturer
The following table lists the additional thruster force amount gained per direction by boosting.
The data is from datamining, which doesn't necessarily represent all stats correctly. But to me it seems to fit pretty good to what you can experience in-game.

ClassManufacturerForwardBackwardVerticalTurning
Artillery CruiserJupiter Arms+250%+100%+125%+15%
Artillery CruiserAkula Vektor+250%+100%+125%+75%
Artillery CruiserOberon+250%+100%+125%+80%
CorvetteJupiter Arms+150%+0%+0%+0%
CorvetteAkula Vektor+200%+150%+40%+50%
CorvetteOberon+200%+150%+40%+50%
DestroyerAll+150%+100%+125%+60%
DreadnoughtAll+180%+100%+200%+250%
Tactical CruiserAll+200%+100%+100%+60%

Some words on interpreting the data: Keep in mind that the base stats not only vary between classes but also between ships of the same class but from different manufacturers.
For example, the Jupiter Arms corvette might look like coming off badly compared to the other corvettes. But it is a lot faster and more maneuverable than the other two right from the start.