I must admit - I have no idea how one embarks upon a career as a diplomat. I think it is because generally speaking many diplomats I have heard of have had non-linear career paths and have various backgrounds.

You might be interested in this then:

http://www.faststream.gov.uk/index.asp?txtNavID=71

in switzerland there is a "diplomat's school" which you can apply to after graduating with a top masters in any discipline. there is a strict entry test and if you pass, you get two years of education - fully paid - before you go on duty as junior diplomat. you will then be sent around the world, never staying anywhere for longer than 2-3 years, for a while. if you then manage to become a senior diplomat you can stay in one country a bit longer.
many diplomats these days work on trade agreements and supranational policy stuff. they don't go to one country but rather form a part of large negotiation teams. you often get people with any kind of economic/legal background in these teams, rather than "trained" diplomats.
there is also the track of the UN - simply apply for an open job there.

Wow thanks for the info.

Recently in Australia there was a bit of a hoopla in the media about a retired/sacked politician who was given a hotly contested diplomat posting in Italy. Some people were saying she deserved the job, others said the PM offered her the position so that she would leave (she did a really bad job as an immigration minister). Still others complained that the post should've been given to actual trained diplomats (or, if I recall correctly, "career diplomats"). That was what got me thinking.