What parameters descibe a gravitational wave? What are the parameters of gravitational waves and how does the configuration of the system that creates those waves affect the result?
My current state of missunderstanding is:

*

*Frequency (due to rotation of two masses areound each other)

*Polarisation (plane, in which the masses rotate around each other)

*Amplitude (mass of objects)

 A: In short, if you are considering gravitational waves from a binary system:
The dominant frequency (it can be more complicated for highly elliptical orbits) is twice the orbital frequency. That in turn depends on the mass and separation of the binary components - approximately through Kepler's third law.
The gravitational waves can be decomposed into two orthogonal components known as "plus" and "cross". Equal amounts of both will be received from a binary viewed with its orbital plane at right angles to the line of sight. Only one polarisation is seen when the binary orbit is viewed edge-on. The degree of polarisation depends on the inclination angle for situations in between.
The amplitude of the waves increases with the total mass of the system and depends on the relative masses of the components (equal masses give stronger waves). Amplitude also increases with the frequency of the orbit and decreases with distance to the source. The amplitude of each polarisation component then also varies with inclination angle, as discussed above.
Edit: For a circular orbit, the observed strain amplitude can be written:
\begin{equation}
h =  -\frac{4G \omega_{\phi}^2 \mu a^2}{rc^4} \left[\frac{(1 + \cos^2 i)}{2}   \begin{pmatrix} 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0\\0 & 0 & -1& 0\\0 & 0 & 0 & 0 \end{pmatrix} \cos(2\omega_{\phi} t)  
       + \cos i \begin{pmatrix}  0 & 0 & 0 & 0 \\0 & 0 & 1 & 0\\ 0 & 1 & 0& 0\\0 & 0 & 0 & 0 \end{pmatrix} \sin(2 \omega_{\phi} t) \right],
\end{equation}
where $\omega_\phi$ is the orbital angular frequency, $\mu$ is the reduced mass - $m_1m_2/(m_1+m_2)$, $a$ is the semi-major axis (which can be rewritten in tems of $\omega_\phi$ and $(m_1+m_2)$ using Kepler's third law), $i$ is the orbital inclination ($i=90^{\circ}$ is "edge-on") and the two matrices correspond to the "plus" and "cross" polarisation resepectively.
