For example, how do they normally sign off letters? We normally use 'Yours Faithfully' or 'Your Sincerely' but we might not be so formal in emails and instead just 'Regards'.
What is standard practise in Chinese for both letters/emails?
It all depends on the formality of the letter or email, the age of person being addressed, his/her relationship to you and how familiar you are with the said person. This is not something that you can define or quantify - you just have to get a feel for it.
Anyway, for letters, the standard valediction goes something like this:
Note the double space before 此致. This is used for someone you don't know (well) and is very respectful.
Once you have acquired a certain degree of acquaintenance with the person, then you can write pretty much anything that one considers respectful such as
Just to list a few.
For emails, the same rules apply; but since they are much more casual, sometimes people don't include any valediction at all. Just type the body and hit send.