XC skiing is not for the inactive, and is far more aerobic than downhill. Its intensity is around that of light to medium mountain biking or light fell-running. The use of the arms though increases the calorie burn about 20% and adds a lot to the demands placed on a brit more used to the arms being less important for sport. Swimmers will have a big advantage here and also in respect of their core muscles in the abdominal belt.
In general I would recommend that you get into some good shape with about 4 to 5 hours erobic training a week if you are a bit ambitious about skiing and the tours you will take, while if you want to enjoyt learning the technique while not wanting to do tours of more than 10km when on holiday then about 2 hours a week running, cycling or swimming in any combination to a level of reasonable intenisty will prepare you enough to help you to enjoy your holiday all the more.
There are some specialist summer exercises and of course there are roller skis. Look up 'Elg Hufing' on y outube or 'summer training for xc skiing' for the very specific exercises if you are pretty serious about it. I would recommend digging out your roller blades and buying some walking poles which are adjustable and light wieght with hand straps which velcro round you like a half glove. I picked up some here for fifteen quid new actually. You will then just add the poles to give extra propulsion in the way ski-shooters do and there are many videos explaining this.
Roller blading is the closest activity to xc skiing in the summer in the uk and has the huge training advantage in teaching you to completely lift the weight of the trailing leg and transfer it to the new leg with a bent knee. With the classic kicking style, you will also transfer all your weight to the propelled front leg when you are doing it most efficiently as you should be taught. The trailing leg is off loaded and consiiously you reduce the contact with the snow until your foot is reaching out for the next stride.
There is indeed one place at least which offers however the real deal in summer and winter time / roller skis of both types in the summer and some forms of snow based training up in Huntly an hour north of Aberdeen at the Huntly Nordic Ski Centre so you could gert into roller blading and then get some training with poles there, and try the kicking style roller skis which have a ratchet mechanism to create the 'tug' from the springing kick.
An important point I should have made earlier is that the principle of the tram line based parallel kicking skiiing is that it is much more about striding and a long gaped run than it is about walking. Walking alone will not prepare your legs and especially your crotch and knees for the long strides / langrenn as the sport is called here / which thrust your weight forward to one foot with a wider angle between your legs than ordinary running.
Walking at 6km an hour, a ,military marching pace, and especially with poles, will be good preparation for your cardiovascular supply to arms, legs and core of the body. If you intend to be a little serious about your holiday and build up to a 20 to 30 km day, then you should be combining a few hours a week conditioning and technique training *more below on that* with walks which get longer in duration. This is tough in the UK as the season for XC beings in the darkest, wettest days, but I have had some great hillwalks or low country path marches at weekends, using most of the day.
Some specific exercises are going to be squats with use of swinging arms too, press ups, sit ups, back 'cobras, high cadence / low pressure rowing machine work and the cylical training machines in gyms they call xc machines but they do not actually simulate it very well in technique, they do involve using your arms.
Stregnth training is about three areas> knees in terms of lifts and holding bent under pressure< thighs, for a springing stride > core training for which pillates is ideal and some breast stoke if you are a swimmer.
The key though is to do some striding with bent knees, like a stride with a lunge > The easiest way of thinking about this is imagine you are in the arctic and have to get across an area of broken ice blocks before the distance between them is too large to jump. You want to stride from one to the next and to be most efficient you do not want to stop on both feet, as you land with your one foot you want to stride off onto the next. The stride will be a gap about half as long again as your usual running span, so probably two to three foot legnths longer. Train up by leaping from one leg only and landing with both legs, and then using the opposite leg. Then move up to striding from one to the next with a slight pause when you land forward on the leading foot, and finally move up to a constant striding motion. Use your arms with palms out reached like spades, taking them long forward on the opposite side to the leg being thrusted forward as in any running or walking, but exaggerate the motion. Don't take your hands higher than shoulder height.
Striding at an exaggerated leap is not something you can keep up for very long, but it will be very very good physical and pre-ski technique because it thrusts the foot forward while it is unloaded completely and needs to be propelled long forward before the weight is unloaded from the other foot. You can however keep up striding to a certain percentage of your maximum you get to in the short bursts, by employing poles where you then assist your body in releasing some weight onto the arms. That is then into @elg hufing@ as they call it here, summer training for langrenn.
This is a really key type of exercise > when striding you will probably be able to string 10 to 20 together without walking poles. Vary then the distance you spring and vary how bent your knees are from the spring to the landing. You can do this indoors while carrying small weights at your side or weights belts to increase stregnth in your legs but employing your arms will help you learn the full body balance. You will also notiice that you employ your core muscles. You can vary then how far forward you incline your body and then do some leap and holds when you stop on the landing foot and freeze your motion with body bent forward and other leg trailing.
In terms of running and hill walking , you can combine this striding into part of your tour. Up hill it will increase your stregnth in your leg muscles and conditioning for the knee most, while down hill it will help a lot with your sense of balance for XC skiing. In both cases we are condsidering a reasonable slope you are going to get a safe and reasonably long stride on without slipping and hurting yourself.
If you are in an alpine ski club or there is a local one, find out if they do conditioning training because the work for your knees and core will pay dividends for XC skiing, where the down hill technique in the tuck is very similar in its basic to down hill, as is ploughing to a beginners slalom and braking course.
Youtube and some of the north american XC web sites are full of good videos on summer and off snow training as well as the actual movements on skis and how they differ from both running and walking.
When you do get to your holiday, given that you have trained semi specifically and not on roller skis, then dont be very ambitious with the amount you do. On the first day your lesson may be 2 hours with an instructor and I would say that you should just do some gentle warm downs on flat surfaces, light strides on the skis as jogging is to running, although you can of course play about on a little down hill by fish boning up and tucking down in the tracks for half an hour or so.
Plan to build up to a goal which is in line with the usual duration of what your find to be a fairly strenous hill walk, bike ride or cross country run.
The striding technique for classic XC skiing with the thrusting kicks and long gate is so very specific to 'langrenn' that you risk getting in particular crotch, knee or lower back injuries if you over do things. Discuss with your instructor after a couple of lessons on what they would recommend for your level of learning / natural ability you have picked up so far, combined with your usual physical endurance condition.