Can someone tell me how to move mail from inbox to folders. Each time I try this, I appear to succeed, only to find out later that when I then delete them later from the inbox, I unfortunately delete the mail permanently.

I've tried writing to gmail, they never respond. Surely in transfering to a folder, they should disappear automatically from the inbox. Otherwise, the same message in in two folders.

Thanks.

There are no folders in Gmail only labels.

After labeling a mail, use the ARCHIVE button to remove it from the inbox :)
If you don't label it, don't worry: you can read it later from 'All Mail'

To add on the advice, with "Labels" you can put the message into multiple "Folders".