Does it need many invaders?
This depends on "how" the invasion takes place. A big military strike versus a well armed(at least same quality of armor and strategic knowledge) nation is difficult and needs some advantages like the element of surprise and a very fast strike of combined forces (see Blitzkrieg for further information). This is probably the most common sense of "invasion".
But also, one could invade a nation by undercutting their government and place some string puppets in their parliament or whatever the government is build in.
So depending on "how" you invade, you have different initial situations.
A military invasion gives the advantage, that you have a lot of manpower in the enemies land which gives you the ability to rule them. You can foist up your law and force them with your military to hold it.
A very effective way to assimilation would be death penalty to everyone who practice a prohibiden religion, language or whatever.
But this can't be enough at its own.
What exactly do you need after a military invasion?
Ban their language, religion and so on.
Your military advantage could act as some kind of police. Therefore compare the occupied European nations during WWII. The German Wehrmacht and SS practically acted as a foreign police. But further you should force the local police to join your guidance. The folks may not like or trust you. The relation to their folksmen in the own police may be better. If the local police-troops don't want to join you, make an example of your power and kill some. This initial step is very brutal and will raise resistance. You must prepare this case. But you should not keep this brutality up for a long run, only at the first time to show them who rules.
Teach them your language, religion and so on
When there is no doubt on your power, teach them your culture in schools. The children are those who accept it very easy.
Show your "new folks" the benefits of the new culture and make them "wanting" it.
For example, as the marks of war are getting less, make tax advantages to those who establish the new culture.
Settle people from your folk in the conquered nation, the more the better.
(3 and 2 can be done simultaneously). People are social creatures. They talk with each other and overtake behavior of other people. Teach your old folks, that the new folks culture is a very very bad thing. Just like Hitler taught the Germans in 1930s that the Jews are pure evil, but they have to understand that the culture, not the people themselves are evil. When they settle in your new country, they will bring up and amplify your culture. Therefore see any multicultural country in the world.
Invasion without military:
Make as many people of your culture settle in the foreign country to assimilate them. This will take many many generations. Therefore so the black/Asian subcultures in the USA. Assume that you can bring at least 1/3 of the folks number with your settlers. Probably doesn't work when the folks 'look' different (skin colour, size,...)
Does the size of the country matters?
Yes and no. If you can enhance the number of folks equivalent to the size of the country, no. Otherwise, a spare populated country like Finland probably is harder to assimilate due culture doesn't spread well and resistance has many improvements, they can hide very well.
Could it be done in less than a generation?
Read upper blocks, depending on the scenario.