Special Relativity - travelling close to light speed When we say something travels close to the speed of light, what is its speed relative to?  
For example, we have 4 highly advanced spacecraft at rest beside each other, labelled A, B, C and D.
We leave A at rest and accelerate B, C and D to .8c.
We can now consider B, C and D to be at rest and that A is retreating from them at .8c.  Considering B, C and D to be at rest we can now accelerate C and D to .8c relative to B.
Can we then consider C and D to be at rest and further accelerate D to .8c with respect to C and continue doing so ad infinitum with an endless array of spacecraft?  
 A: Yes we can. According to special relativity, all inertial frames of reference are equal.
What might seem as a paradox here, is that if C is travelling at $0.8c$ with respect to B, C should be travelling at $1.6c > c$ with respect to A, which is a contradiction. However that argument is flawed, because the correct formula for addition of velocities in SR is
$$ w = \frac{u + v}{1 + \frac{uv}{c^2}}$$
According to this, velocity of B with respect to A is $v_{B:A} = 0.8c$, $v_{C:A} = 0.976$, $v_{D:A} = 0.9973c$ ... It is rather easy to see that if the relative velocity of n-th spaceship with respect to first is subluminal, then also n+1-th has a subluminal velocity:
$$  w = \frac{u + v}{1 + uv/c^2} =
c + \frac{-c - uv/c + u + v}{1 + uv/c^2} =
c + \frac{-c(1 - u/c)(1 - v/c)}{1 + uv/c^2} < c
$$
A: 
When we say something travels close to the speed of light, what is its
  speed relative to?

Left unspecified, it is generally understood that the speed is relative to the frame of reference in which one is at rest.  However, it's better to explicitly specify the reference frame with respect to which some object has a relative speed.
For example, one might write "twin A observes twin B to have a speed of 0.8c" or better, "twin A & twin B have a relative speed of 0.8c".
In the case of 4 spacecraft, there is a relative speed between spacecrafts A & B, A & C, A & D, B & C, B & D, and C & D.  Indeed, each spacecraft has a speed relative to an infinity of inertial reference frames.
So, unless the context is clear, it's best to explicitly identify with respect to what a speed is relative to.
A: Yes, but the difference with Galilean relativity is that velocities are composed using the "rules" dictated by special relativity.
A: Whether you need relativity depends on whether the parts are moving fast relative to each other (or relative to some fixed frame that you do your calculations in).
Let's see how by exploring a common fact about non relativistic situations, the mass of a system in nonrelativistic situations seems to be very very very close to the sum of the masses of the parts.  So what is mass?  Well, it's not a fundamentally conserved quantity (or even an extensive property) like energy and momentum.  Energy and momentum are fudnamental and mass just tells you how the two relate to each other when the particle is on shell, but being on or off shell is a quantum thing so let's ignore that.  What do I mean by fundamental?  Well, the energy of a system is the sum of all the energies in the system and the momentum of a system is the sum of all the momentum in the system (include the interaction energies and interaction momentum).
But wait, I said that mass says something about how energy and momentum are related!  Yes, $(c^2m)^2=(c\vec{p})^2+E^2$ and that left hand side is how we compute the (squared) length of the energy-momentum $(E,c\vec{P})$ in relativity.  The energy-momentum vector points in the same direction in spacetime that the particle travels. And the geometry assigns a zero squared length to things moving at light speed so that the geometry (which preserves length) can preserve moving at light speed so that everyone can agree on it.  The price to pay is that some vectors have a positive squared length and some have a negative squared length and some have a zero squared length even though they are not the zero vector.
OK, so if a bunch of stuff is all moving at similar speeds to each other, then their motions each have vectors and al those vectors are pointing in almost the exact same direction in spacetime, so their energy-momentum vectors are all pointing in almost the exact same direction inspacetime.  So when you look at the total energy-momentum vector for the system it points in almost the same direction as everything else and even nicer it's length is almost equal to the sum of the lengths of the individual vectors that added up to make it. Those parts might all have different individual masses, so different length energy-momentum vectors, but since they had low speeds relative to each other, their vectors pointed in almost the same direction in spacetime, so the length of their sum is approximately equal to the sum of the lengths.  Mass is just the length of that vector.
So when things move slowly relative to each other, the mass of the system is approximately equal to he sum of the masses of the parts (because the length of a sum of vectors pointing in almost the same direction is approximately equal to the sum of the lengths of the individual vectors). So this nonrelativistic fact that the mass of a system is the sum of the masses is technically false, but it approximately holds when they have low speeds relative to each other.
Every other fact of relativity and nonrelativity is the same. There are real rules (the relativistic ones), you can learn them if you are willing to give up your old assumptions and spend time learning the new rules and these new rules reduce to approximations of the old rules in the special case when all the vectors describing the motion through spacetime are pointing in almost the same direction.
