How do I manage 'other' storage on my iMac? i have a 500gb flash storage of which 390gb is 'other'. Yesterday I deleted 50gb of dmg files but this morning it doesn't seem to have made any difference

In short, you don't. The OS manages the 'Other' category.

Read this:

https://support.apple.com/en-ca/guide/system-information/syspf9b375b9/11.0/mac/11.0

and note the following:

Other: Contains files that don’t fall into the categories listed here. This category primarily includes files and data used by the system, such as log files, caches, VM files, and other runtime system resources. Also included are temporary files, fonts, app support files, and plug-ins. You can't manage the contents of this category. The contents are managed by macOS, and the category varies in size depending on the current state of your Mac.

One easy method to free up storage space is to move your Photos library to an external disk Move your Photos library to save space on your Mac - Apple Support

Also make sure you’re emptying the trash when you delete items.

There are articles to be found on the internet detailing which cache files can be manually deleted to address the ‘other’ issue, however this may be best left to the more experienced user.

I use the built in Storage, Manage process to tidy up.

I have read that leaving the computer running all the time doesn’t allow some background maintenance tasks to take place. So if not already doing so try turning the computer off a night for a few days to see if it improves things.

I have an M1 iMac with a few apps installed which I only use periodically and I find that daily use like browsing, email & streaming videos have not produced a big ‘other’.

I have the same problem with other taking up 397gb on my SSD causing problems with rendering after-effects and even Illustrator. I don't do a lot of rendering and mostly just use Illustrator, I don't have anything in Photos or Music not even 1 song, I am not into social media, I have freed up space like directed but It seems that the more space that's available on your SSD the more space other will take up! I have wasted so much time trying to solve this problem that I feel I have no option but to reset my iMac back to factory default and start again!! bearing in mind my iMac is only over 12 months old it's a bit laborious. Is there a solution to this?? or does Apple have to consider putting in a separate SSD for other to run on, so your storage space is as it's intended to be just storage!!

Restart in Safe Mode

https://support.apple.com/en-gb/HT201262

this will clear out some chats and other temporary files.

Chats? I meant Caches...