How to model non-linear regression I am trying to learn how to modell data (x and y) that looks when plotted like this:

Can someone perhaps recommend any good literature or video series on how to do such task?

This looks like a discontinuous response to discrete controls. The first regime ($R_1,$ I'll call it) is in $x\in[-20,-12.5],$ the second $R_2$ is $x\in(-12.5,-3.5],$ and the third $R_3$ is $x\in(-3.5,20].$
For $R_1,$ I would go for a decaying exponential. I would fit
$$y= a e^{bx},$$
or equivalently
$$\ln(y)= \tilde{a}+bx.$$
For $R_2,$ it again looks like a decaying exponential, so I would fit a similar function:
$$\ln(y)=\tilde{c}+dx.$$
Finally, in $R_3,$ it looks like a damped sinusoid, so I would do the non-linear fit
$$y=e^{gx}\,[h\cos(jx)+k\sin(jx)]. $$
It would help if you are able to determine $j$ from a peak-finding routine. It looks like the period is about $7,$ so you could try
$$j=\frac{7}{2\pi}.$$
It also looks much more like a $\cos$ than a $\sin:$ you might be able to get by without the $\sin$ term, which would turn your problem into a linear regression.
