I'd say high score is only a very small part of HoF play, the majority still focusses on achieving the various victory conditions with the fastest possible finishing date, regardless of score.
That said, if it's high score games you're interested in, you have to grow big just under the victory condition (e.g. domination land limit) and finish exactly the turn where the added score from population growth would not make up for the lost score due to finishing a turn later anymore.
Recently, it was discovered that the domination threshold can be increased by creating lots of dead AI (many more than the number the game was started with) by having them spun off as colonies.
Here's a list with a wild mix of different HoF writeups compiled by
@Seraiel
https://forums.civfanatics.com/threads/compilation-of-hof-writeups.547062/
I can only recommend playing some HoF games to everyone really. Although I never submitted much, it has been a very important part of my Civ journey so far. The style of play is really unique in that on one hand you can play really risky early turns and "plan" for things such as a convenient horse location, a successful worker steal, etc., knowing that you can always discard the game and start over if doesn't go your way. On the other hand, a game quickly becomes too valuable to discard and you transition to more of a "make no mistake"-playstyle like in a BOTM setting. Both HoF and BOTM offer a rewarding sense of achievement due to no reloading/replaying, but HoF takes away the pressure to perform from turn 1.
Another thing worth noting is that by far not all HoF play aims for the top table. Some of the challenges are crafted especially to add extra difficulties or interesting choices. For example, one challenge game by
@lymond which I remember fondly because it resulted in my first win on deity, we had to achieve a religious victory but had to include Togukawa as one opponent, thus finding a way to overcome his stubbornly closed borders was essential. Another example was playing for conquest with Persia on an Oasis mapscript (player always starts south, horses are always north, do you cross the desert with your settler? You can reroll maps after AH quickly ofc.). This resulted in a welcome change from Mapfinder starts.
Btw, Mapfinder is a fun tool regardless of HoF. Recently, I used it deliberately to find horrible/tundra starts for me to suffer through.
