Hill walking fitness is something that has to be built up over a long period of time, but it is really easy to build up your basic level of fitness to make your days out on the fells far more enjoyable.
Your lifestyle, occupation and where you live all have a large effect on what and how much you can do to improve your basic fitness for hill walking.
Time on your feet: Whether it is walking part way to work, or having a blast around the block on a weekend, increasing the time on your feet each week will have a huge effect for when you head to the hills and walk for several hours.
Building basic fitness: Government recommendations state that everyone should do 30 minutes exercise a day to maintain good physical and mental health. This is not always feasible, but the more of this you can do the greater your basic level of fitness will become. You don't necessarily need to join the gym or go running; anything that raises the heart rate counts!
Start easy and build it up: Don't jump in at the deep end when getting out onto the fells. Take on a couple of fells that you know are within your reach before pushing your boundaries, a little bit at a time. The mountains aren't going anywhere, so why not build up to tackling that challenging one when you know it will be nice and comfortable for you.
Specific Exercises to Improve Hill Fitness: The main area to focus on is building up the stamina in your legs and your core, as well as your cardiovascular fitness. Specific exercises include Squats, Lunges, Calf Raises, Stepping exercises, sit ups and leg raises. If you can get out on a bike, for a run or a fast paced walk every week then this will all contribute to building your aerobic capability.
Remember to Warm up and Cool down before and after every exercise session. Start with low repetitions/ distances and build it up each week, remembering to have rest days.
Finally the most specific exercise is getting out on the hills!