There are cases when you can't just delete the old version of the mod and add the new one - it will break, the game will spit bugs at you and you'll have no clue what the heck is going on. To prevent such misfortune from occurring, please read the following before you update the mod.
Updating to 1.21
Because the differences from 1.20 and 1.21 are so extreme, you will need to clear out any datapacks in your world. Follow the guide below (My world won't load!) for more information.
Major updates
Some major updates may rework the structure of configs, and cause old configs to be incomprehensible to new versions after such an update, resulting in unpredictable behaviour. To avoid this happening, the game will automatically delete your old configs.
If you have modified the configs in any way, recall and save your modifications (for a guide on config modification, check this wiki entry). It will automatically restore the folder with all the modifications the update brought. After the folder has been restored, you can go ahead and reimplement your changes to new files. Don't just replace the files with old ones, especially the root infinity.json, instead edit them and reinstate the changes, as replacing the files might cause the mod to detect them as old configs and revert back to default. I might implement some code to merge changes like that automatically in the future, but for now it is how it is.
If you never modified any configs, you should be able to update the mod normally.
Minor updates
When the update only differs in the last version number (i.e. 1.5.3 to 1.5.4), you are completely safe from all the dangers above. However, even minor updates can alter generation of specific dimensions in such a way that old seeds (book texts) will lead to completely different generation after the update. This, however, won't break existing dimensions in your existing worlds, as all data for them is already generated; even new chunks generated in them will be consistent with old ones.
My world won't load!
If your world won't load even after deleting your config/infinity files, or if you are updating from a dramatically different version like Infinite Dimensions 1.0 or Minecraft 1.20, you may need to manually clear out the old datapack files. With Minecraft open, select your world and choose Edit. Click "Open World Folder", and delete the datapacks folder. You should now be able to load into the world. If this does not work, please report it to the issue tracker.
If you are playing on a server, you can delete the files from inside your world/datapacks folder.
To access your old dimensions after this point, you will have to reopen the portals that lead to them (by right-clicking them). All the chunks, blocks etc. already placed in there will remain in place, the only thing that might get reset is biome data.