A Cairn is small, and that is where the resemblance to a small dog ends. He was made to go into the ground after something that could hurt him, alone, and to decide for himself once he was down there. Everything below comes from that.
Exercise
An hour a day for an adult, in two goes, and more if you have it. But a tired Cairn and an occupied Cairn are different animals: half an hour of using his nose tires him more thoroughly than an hour of walking, and a bored Cairn will find his own occupation, which you will not like.
The nose leads
When a Cairn is following a scent he is not ignoring you — he genuinely cannot hear you, in any sense that matters. This is not disobedience and it does not train out.
So train the recall as a competition you have to win rather than an instruction he should obey: pay it well, pay it every time, and never call him for something he would rather avoid. And be honest about where he is off the lead. Near a road, near livestock, near a hedgerow he has already noticed — the lead is not a failure of training.
Digging, barking, hunting
Three jobs he was built for, and none of them will be trained away. What works is giving each one somewhere to go.
Digging: a corner of the garden that is his, or a sandpit with things buried in it. He will use it, and he will use your borders less.
Barking: he is telling you something is happening. Teach him that you have heard — go, look, thank him — rather than that barking is forbidden, which only makes him bark at you as well.
Hunting: scent games in the house, a snuffle mat, food hidden about the garden. Earthdog work if you have it near you.
Other animals
Cairns and cats often work, particularly if they grow up together. Cairns and small caged pets are a different matter, and it is fair to say so plainly: a rabbit, a guinea pig or a hamster is prey to this breed, and no amount of training makes it otherwise. Manage it with doors, not with hope.
Children
Good with them, and better with children who have been taught how to behave around a dog than with a dog taught to tolerate anything. A Cairn will remove himself when he has had enough — give him somewhere to remove himself to, and teach the children that when he is in his bed he is not available.
Being left
Build it up from minutes. Most adult Cairns are content alone for three or four hours if they have been walked and left something to do. A puppy is not, and the first weeks of leaving him are best measured in ten-minute increments.
Grooming as a habit
Ten minutes a week — see the coat — rather than an event twice a year. It also means you have your hands on him regularly, which is how lumps, ticks and sore ears get found early.
Where to go in Luxembourg
The Alzette valley paths, the Mullerthal trails, and the forest tracks around the country all suit a Cairn: varied ground, plenty to smell, and a lead when livestock or a road is near. In town, the parks are fine, but a Cairn on a pavement is a dog waiting for the interesting part of the day.
And at eight years old
Nobody asks this before buying a puppy, and everybody finds out. A Cairn ages well: less distance, the same opinions, and a strong preference for the warmest spot in the room. The nose keeps working long after the legs slow down, which is why the scent games you start with a puppy are the ones that still work when he is old.