If you do the LDWA events regularly you may not need to train! Otherwise read on
Firstly you need to be able to do the distance comfortably, so doing some long local walks, get used to the stamina needed and make sure your boots don't give you blisters on long walks.
Secondly, the more aerobically fit you are the quicker you will ascend the hills, so if you want a good time do some aerobic training. I have done it 20 times. I once did it after working out on a rowing machine for a year and completed it in 6 1/2 hours. That was over 20 years ago, my last time was pretty close to the 12 hours max
From experience of our walking club, anyone who walks every week 10 to 15 miles will be able to complete the 3 peaks with no distress.
The main thing is to be fit enough to enjoy it as its a great walk.
It such a shame to see people doing it who are hating every minute because they are unfit.
A lady in the Ramblers association did it on her 70th birthday. And again on her 80th! How about that?