Right to access in Scandinavia
The right to access is in some countries the right for anyone to vastly partake of nature and what it offers, as long as it is within the boundaries of local law or general acceptance. Although Scandinavia is quite expensive, many of the things that are of most value are free-for-all – the scenery, hiking, quite a lot of museums and many other sights.
Not only that, for those who feel like camping, in Norway, Sweden and Finland it is generally possible to camp freely in the woods and in the mountains. In these three countries, laws have been enacted guaranteeing "Every Man's Right" to access uncultivated lands, or these rights are considered customary law.
Given knowledge of these laws and camping equipment, it is in fact possible to travel rather inexpensively in the Nordic countries.
Obviously any law that comes with such a right also comes with responsibilities and some limitations. For organized events or commercial activity the rules may be somewhat stricter than for individual hikers. The right to access may of course be limited in nature reserves and the like.
Walking and passing
In these countries, you have the right to walk across uncultivated lands. That means you can walk if there aren't any farmlands or you're not crossing people's gardens. If there are fences, you should look for gates and follow paths, also if there is no apparent farmland (there might be animals, such as sheep or cattle in the area, so always close any gates you open). Also, if there are newly planted trees in an area, you can't walk through. Other than that, you can pretty much go wherever you like. Fields may also be crossed using existing paths and when they are covered with snow (and risk no damage).
Camping and picnicking
Camping is allowed for one night in Sweden, in Norway two nights in normal countryside and as long as you wish in the wilderness, in Finland "temporarily", which means at least one night and at least two nights if you behave, probably more in the wilderness. You should not camp near houses or farmlands, where "near" may mean 150 metres and far enough that you do not inconveniencing anyone and particularly not those in the nearest house. As long as you keep out of the way you should be OK.
These regulations obviously don't go for those areas especially designated for camping, but those are usually paid campsites.
If 'out of the way' sounds harsh, it really isn't. There is a lot of free space in Norway, Sweden and Finland...
Pretty much the same rules apply to picnicking.
Rules about camp fires differ between the countries. At least you must not cut any trees or risk wildfire. The camp fire must be built in such a way that the fire does not spread and fire must not be made when forest fires are likely (according to weather forecast). Always make sure you have water nearby so you can put out any tinder or fire when you leave. When you leave, make sure the remnants are cool and removed or hidden (unless you used an existing fire place). Do not make the fire on smooth cliffs, which will crack, or peat, which is hard to extinguish reliably. Leave no trace.
In Sweden camp fires are allowed as long as you are careful. In Norway camp fires are not allowed in or near forested areas in the summer. In Finland you generally need landowner permission, but making fire is often allowed on state owned land in the north by separate decisions.
Living off the land
It is generally OK to pick wild mushrooms and berries, unless they grow in apparently cultivated areas. In Norway, you can also pick wild nuts if you eat them on the spot. However – there are really nasty mushrooms, even lethal, and some of those resemble edible mushrooms of other parts of the world. If you plan to pick mushrooms, buy a good mushroom guide. They are generally quite expensive, but worth their price. There are also poisonous berries, but few that cannot easily be distinguished from edible ones.
Please note: fishing is restricted and hunting always requires licence and permission. Some fishing is allowed without licences, but what fishing varies by country and type of water. Check with the local tourist agency.
Note that picking cloudberry, an orange raspberry-looking arctic delicatesse, is strictly regulated in northern Norway. Picking and eating a few berries is always allowed, though. Also in Finnish Lapland commercial cloudberry picking may be restricted.
Leave no trace
Whatever you do and wherever you go, it is still your responsibility to leave no trace of your visit. This means you should leave no garbage behind, make sure the camp site you used looks as good when you leave it as when you came. Do not break off any trees. This is the responsibility you get in exchange for the right to access.
In Sweden, the "Allemansrätten"  as it is called, is not based upon a formal juridical passage, but on a general acceptance.
In Finland, the "Jokamiehenoikeudet" or "Allemansrätten"  is similarly part of customary law.
Along many popular tourist roads and spots, there are "no camping" signs. These are there to avoid a heavy impact on areas which are particularly popular, and should be respected. Just go a few hundred meters further, make sure you're out of the way, and you're OK.
Although camping vans are OK, it is generally, if usually silently, frowned upon just parking them in a parking area and staying overnight. Obviously mountains and other extreme areas are paved as little as possible. Parking areas are therefore deliberately a scarce resource, and should be used only for parking, not for camping. If you're using a camping van, use paid campsites.
Note that around some cabins in the more popular mountain regions such as Jotunheimen in Norway, extra limitations have been set up which prohibit tenting up to 2 km from the cabins. This is because campers have used sanitary facilities in the cabins without paying. Many Norwegians believe that these limitations are illegal and so blatantly ignore them (and love to be taken to court to have it struck down). They have not yet been tested in court, however, and as a foreigner you might not want to argue about it, so you might want to comply. However, if you do camp, don't use the facilities of nearby huts without paying the dues. In short: around most cabins you can camp as close as you want (or in a designated area) by paying a small fee – you then also get access to the cabin's facilities. If you don't want to pay, you'll have to go 150 m away. Around some cabins you will have to go even farther away.