Germany, women and men:
National level:
1. Bundesliga (national league), 2. Bundesliga, 2x 3. Bundesliga (north and south)
Below that but still on the national level:
Four regional leagues (Regionalligen, fourth division?)
Eight Oberligen (don't know how to translate that, fifth division?)
State level (although we have only 16 states we have 18 associations)
Each association has:
State/association level leagues, district/county leagues and administrative district leagues (the last two are usually divided into so called leagues and lower ranked classes)
e.g. in North Rhine-Westphalia we have at the state level:
Women: 2 NRW leagues, 4 Verbandsligen (something like association league)
Men: 3 NRW leagues, 5 Verbandsligen and 11 state leagues
Seniors women/men: NRW leagues 40+, 50+, 60+ and 70+
Cadet women/men: NRW leagues <=13, <=15 and <=18
How to move up and down: It depends... The first team of a league usually goes up and the last team goes down and depending on the league, the teams in second (and third) place play relegation matches.
New teams: You can always start in the lowest league and, of course we're in Germany, there are regulations on how and if your team can start in a higher leagues.
New players: We have something similar as the USATT ratings called TTR. Initial TTR: Depends (we have regulations...) either your club assigns you to a team and a position in that team then you will get the average TTR of all players in that league and at that position (roughly, it's a bit more complicated) or if you start at a tournament then it depends on how many matches you win (and of course which rating your opponents had and there is a lower limit depending on your age and...
We have leagues with 6 players per team, leagues with 4 players per team, some have only 3 players per team and what not...
Oh, we have some more regulations: Your position in a team depends on your TTR rating and the position in your team determines/can determine (it depends, we have some more regulations) which whom you have to play doubles in a league match...
https://nrw-tischtennis.de/wp-content/uploads/2019/12/WO2020-01-01.pdf (only 84 pages for NRW)
https://www.ttvb.de/wp-content/uploads/Kurzbeschreibung-TTR.pdf (short description of TTR ranking, 8 pages)