I am confused by the use of 'myself' in a sentence where 'me' would appear to be more appropriate.
I came across an articel in a local newspaper recently that said
'I am looking for a confident and experienced P.A. to run my private office and support myself....'
This looks and sounds wrong to me.
Would anybody be able to define the rule for the use of myself.

Paul,

Use "-self" words for two reasons: to refer back to the subject and to add special emphasis.

Referring Back to the Subject

He cut himself accidentally.
We treated ourselves to dessert.
The doors in the haunted house appear to open all by themselves.

In each example, the -self word refers back to the subject (He-himself, we-ourselves, doors-themselves).
Adding Special Emphasis

I did it myself!
The teacher herself had to look up the answer.
We designed the website ourselves.

In these examples, the -self words could be left out and the sentences would still make sense. The words are there for emphasis only.

I hope that helps. (Thanks to www.writing911.com whose examples I 'borrowed'.)