I've been in the field almost a decade. I dont know first hand whether the route I took would still be the best, but here goes.
After I did my A-levels I went to university for a computer science course. Nowadays I'd replace that with something with less mathematics and more hands on, say 'Computer Systems'.
While doing that degree course, I messed around building PCs or just opening up PCs and finding out how the entrails worked. The kind of thing any gamer who builds his own PC does nowadays. I build a little network of 3 PCs, one of them a server. That gave me some knowledge of ethernet, windows domains, mail server software, etc. All the typical stuff businesses run. Basically, replicate an office environment and play with it.
When summer came, I looked for a summer job in a small local computer company. Thanks to all the playing around I was able to say I had knowledge of all the business applications above, so they hired me for a summer job. There I got hands on experience working in real scenarios. Troubleshooting, installing, etc. Most clients were small companies with 5 to 20 users and one or two servers. I remember I did everything from programming, to websites to fixing PCs to installing ethernet cabling in an office, including the patch panels where all the cables meet (structured cabling). I got quite dirty at times
My plan was that experience would help me get employed elsewhere when I finished my degree, but the same exployer made me a good offer, without even needing an interview since they already knew me, plus I could return to my home town rather than go to London and feel miserable in the tube every morning, in a specifically programming job. (I grew to like the variety of being a jack of all trades in a small company).
To cut an already long story short, from there its all about establishing working relationships through clients and you end up moving on to better jobs progressively if you play your cards right and above all continue learning. 3 jobs later I work for the local government I.T. Department. I never get to open up machines any more. Well maybe some servers when installing them.