There is definitely a lot of confusion over this issue. Mostly because some of the laws are absurd!I was 16 last September and took my tractor test soon after. Firstly the tractor you take it on can't be more than 2.45 metres wide (at the widest point i.e including mirrors etc.) All the lights must be in working order and you can't have anything on the back of the tractor. You can drive to the test site unnaccompanied but you must have L-plates front and back. If you fail the test you can still drive the tractor home unnacompanied! You aren't allowed to practice on the road, the only time you are allowed on the road, before you pass your test, is on the way to or from the test site.
At the test itself the examiner doesn't come in the cab with you he stands by the side of the road and watches you. I had to drive up and down a few times, reverse round a corner, do an emergency stop, stop in appropriate places, drive round roundabouts etc etc. Then he asked me a few questions on road signs and a bit of general driving theory and that was it.
Once you've passed your test you are still limited as to what you can drive. Tractors and implements/trailers must all be no wider than 2.45 metres. Any trailers must be single-axle or double-axle as long as the centres of the axles are no more than 1.3 metres apart (no artics). There is no limit on the weights you can tow/carry other than the limits everyone has to apply to. Having said all this I can't see a policeman casually stopping you, checking age, licence and then measuring your trailer width and how far apart the axles are. As long as you are driving sensibly it should be fine.
To apply you need to have a provisional licence and then just ring up the DVLA (0300 200 1122 is the number you need I think) and ask for a tractor test (Category F). They should send you an email with date and time but keep checking the website as I didn't get my email. It could take a few weeks for them to get everything sorted depending on how reguarly people in your area take tractor tests!
Hope this helps and if you have any other questions I'll do my best to find the answer to them :)
By the way as far as I know when you get to 17 these width restrictions are cancelled but I'm not certain on that.
Good luck with the test!
JS