The anti-immigration people in Finland are quite pessimistic about immigrant integration in general, which is understandable considering that Finland's - and Europe's integration record has not been good lately.
Yet there are a few countries that are integrating a lot of immigrants successfully, and more countries that are integrating parts of their immigrant flow fairly well.
Israel has taken 1.2 million immigrants between 1989 and 2004, and integrated them fairly successfully. The US has acquired 1 266 264 new legal permanent residents in 2006, and is doing pretty well with them too.
By "pretty well" I mean that the immigrants are doing well financially and educationally. I don't mean that there are no problems at all. Russian mafia and Vietnamese gangs are a problem, but one is not afraid to walk through Russian or Vietnamese neighborhoods. Islamic extremism is a problem, but Muslim immigrants graduate from colleges and find good jobs at about the same rate as the general population, and at a higher rate than native-born Muslims.
There is a fairly serious concern about the illegal Mexican immigration now, for several reasons: first, people resent illegal immigration just because it is illegal, and are uncomfortable with porous borders, second, people doubt that the US integration capacity is enough to assimilate many millions of immigrants coming all from the same country.
But in general, US had done well with immigration, Israel has done well, and UK seems to have done well with some of its immigrant groups, such as Indians. It can be done. Here is a list of what I think are the important factors here:
1. Get the right people. Out of the 1.2 million that immigrated to Israel in 1989-2004, 82% were Eastern Europeans. I don't mean that Eastern Europeans are the way to go, but if you admit the folks who are not integrating anywhere else, don't hold your breath here, either. The more backwards the country of origin is, the more educated the immigrants themselves should be.
This is not to say that you can or should always select the immigrants well. If a Finn, for example, wants to marry a foreigner and the foreigner in question is neither a criminal nor a threat to the national security you have to admit them, even if they live in a tree and don't know how to use a toilet. When you are taking large groups of refugees or workers, however, it's possible and it's better to select ones that actually can integrate.
2. Welfare state and refugees are a bad mix. I think that the most essential reason for the USA's success in refugee integration is that they simply know that if they sit on their asses they will eventually run out of money.
Living on welfare for a long time is bad for people in general. It is especially bad for the kind of people who don't know any locals, don't have any useful skills, and did not grow up with the concept of welfare. Learning a new language, finding a new job and building a new life requires a lot of work, and a lot of people are tempted not to do that work if it's not completely necessary. The knowledge that they are going to be fed forever, whatever they do or don't do, is not going to encourage them.
I am not sure what a welfare state can do about it if it intends to stay that way and still wants to admit refugees. Use the welfare as a pressure to integrate as far as possible, probably.
3. Immigrants' tendency to settle in the same areas has both its benefits and drawbacks. The benefit is that they learn from each other and build up a reputation for themselves. The drawback is that, well, they learn from each other and build up a reputation for themselves.
My father found a professional job 3 months after arriving to the US, and in spite of his very bad English. My mother found a professional job 6 months after arriving to the US. One important factor there was that there was a lot of Russians in the area, their prospective employers and all the other employers in the area already had some Russian employees, and they either knew that the univeristy they graduated from was a good one, or knew whom to ask. My parents benefitted from having all those other Russians around who came before them. If they belonged to a group that had a bad reputation locally, they would have probably benefitted more from moving somewhere where there are fewer of them.
If a group is well-integrated, having a lot of them around contributes to the newcomers' integration. The people who came before you recommend you to employers, introduce you to their local friends, tell you how the things work, etc.
If a group is badly integrated, having a lot of them around inhibits the newcomers' integration - or integrates them into the wrong parts of society. The people who came before you tell you how to work the welfare system without doing any useful work, and introduce you to the local drug dealers or whatever.
Splitting an immigrant group into small groups and putting them into different communities has some benefits, at least for the kind of groups that tend to produce youth gangs, but it also has some problems: elderly immigrants need services in their own language, and providing such in a lot of different places is quite expensive. Splitting families is quite problematic too. Putting all the grandmothers into one place while simultaneously putting all their grandsons in different places and ensuring that the grandmothers are not very far from the grandsons is not a trivial task, although it can be done in a sufficiently large metropolitan area.
4. Getting immigrants to consider themselves real members of the nation, and everyone else to consider them so, presents three challenges.
First of all, it requires some kind of positive nationalism. Everybody involved should believe that the country in question in something one should want to be a part of. Second, the national identity should be open to new members, and not, for example, be restricted to the indigenous ethnic groups only. Third, the national identity should not be open to everyone who just happens to live in the country, but it should be something that is achieved by integration and naturalization.
"Our nation is really great, and you can be a part of it", as they usually say or imply to the immigrants in the US and Israel, might sound silly, but it sure works a hell of a lot better than "our nation is small, cold, full of unfriendly racist people, has a language that's almost impossible to learn and we don't really understand who would want to become a part of it anyway".
Mind you, people all over the world complain about their countries every once in a while, and Finns are no exception. But "this place totally sucks" is not something you want to tell the new immigrants on a regular basis. Especially since it doesn't, in Finland's case.
I realize that most Finns would feel silly saying that this is a land of freedom, opportunity and democracy, even though this is the case, at least to the extent that it normally is in the Western world. One does not, however, need to keep repeating that this is a shitty place, especially since it is not really the case. One especially does not need to tell the immigrants "there must be something wrong with you, otherwise you would have never moved here".
Trying to restrict membership to the indigenous ethnic groups only is also a barrier to integration. "Most Somalis won't integrate very well" is a realistic prediction based on previous experience with Somali integration. "A Somali cannot ever integrate" is a self-fulfilling prophecy.
Finally, integration is something that an immigrant does. One does not become a Finn - in any sense of the word - just by moving to Finland. Integration is partly a passive process - places have their ways of changing people - but mostly it is something that the immigrant works on (by learning language and other skills, learning how things work, finding a job, meeting people, etc.) and is rewarded for (the reward being a normal life, job, friends, etc.). It is not something that can be given to a person, at least not to an adult person.