You mentioned dyeable gear, so I'm guessing maybe that's the main thing you're there for.

If there is still an "NM train" running in Anemos (ie. all players converging onto FATEs), that's the quickest way to get good amounts of crystals for upgrading your gear.

The exact etiquette for getting into parties will vary according to your server - on Elemental (JP) people will "put their hand up" in /sh chat with a "ノ" symbol (or "/" seems to work too) to indicate they're looking for a party once an NM location is called, and then the group will disband afterwards.

You might need to be selective about which gear you actually upgrade, depending on how hard it is to get crystals.


Also, for leveling up, the Challenge Log gives good EXP - but trying to do it solo is a long tedious business. If you can pair up with someone of the same level, you can get it done at least twice as fast since you both get credit for each monster killed (and don't take as much damage, so less time spent healing). And of course a whole party is going to be much faster again.