I have many passenger cars, running on a hybrid Digital and Analog voltage. I have many older locomotives that I cherish, and more digital loks I also like. therefore, I either run from a digital trafo or a analog (older style) trafo. The lights in the passenger cars flicker and I know installing a capacitor will act as a steady battery and the lights will not flicker anymore. What capacitors should I use, and how are they to be installed? Also, I use current conducting couplers...

For analogue operation and reversing voltages, better pick a 50 V capacitor. A resistor that limits the inrush current and a diode are useful add-ons.
Only use capacitors for DC, i. e. behind a rectifier.
You probably mean 470 µF or 0.470 mF.

Long story short: difficult to recommend flicker protection without knowing what types of lights are installed.

I found diagrams on German websites. I hope they help - along with automatic translation.

https://www.bahnjockel.de/pufferspeicher.html
https://www.1001-digital...trolyt-kondensatoren.php

The diagrams are from two-rail websites. As mentioned before, a 50 V capacitor should be able to handle the reversing voltage of analogue AC operation.

I used a pair of 50v 1000 uf capacitors in my tinplate carriages which operate on both analogue and digital by way of tiny bridge rectifiers. No flickering on a 5 coach consist with one pickup shoe and connections through 1.25 twin sockets. In my first conversion, i used one car as a master with the resistor and bridge supplying all other cars, but each car has2 of those capacitors. They are big, but I found smaller uf wasn't anywhere as good. If you fit them up under the roof, you cant really see them. I also used strip LEDs. On later plastic coaches with current carrying conductors, I started using capacitors, resistors and bridges in each coach. Only flicker with them was caused by the conductor couplings.