Finland had spent the past hundred years as a Grand Duchy of Russia, and beyond that something of a recurring tug-of-war between Russia and Sweden it seems, so Independence seems like it would have been a new thing for them, not like, say, Poland which had antecedents to look to in its historical past.
So following independence, how did Finland work to create a new Finnish nation and people?
[Interwar Period - Scandinavia - National Identity]
Hi there, and apologies for late answer - been on a vacation and away from computing devices!
This is an interesting question, mainly because Finland's status during the "Czarist era" (1809-1917) was fairly interesting one. Unlike most territories conquered by the Russian Empire, Finland was allowed considerable autonomy from Russia, to the extent that by late 1800s, Russia was mostly responsible for defense and foreign affairs while Finns handled the internal affairs of Finland pretty much the way the Diet of Estates (parliament, with largely hereditary representatives drawn from the four estates of nobility, clergy, burghers and peasants) and the Senate of Finland (an organ that combined the functions of a cabinet and supreme court, and whose members had to be Finns) saw fit. The autonomy resulted primarily from two factors: one, czar Alexander I had wished to prevent Finland from slipping back to Swedish sphere of influence, which could have been a real possibility, and two, by 1860s Finland had demonstrated her loyalty to the Russian crown, even when the Crimean War and the rebellion in Poland would perhaps have provided an opportunity for secessionists.
As a result of this considerable, even surprising degree of independence, Finland was already well on her way towards nationhood by 1917. Finland had had her own currency and central bank since 1860s, and had been the first country in the world to offer both universal suffrage and eligibility for being elected to the new unicameral parliament in 1906 (New Zealand had offered universal suffrage slightly earlier, but women couldn't be elected). In some ways, the declaration of independence was therefore a simple affair - at least in theory. The Finnish interpretation was that Finland was not part of Russia but in a personal union with the czar Alexander I and his descendants, and it was actually this interpretation that undergirded the Finnish declaration of independence in 1917 - the (official) justification being that since czar Nicholas II had abdicated, the Senate of Finland will henceforth assume supreme power in Finland.
By the time of independence, Finnish national identity was already fairly well developed. Culturally, linguistically and politically, Finland was clearly separate from the rest of Russia. The czar had actually promoted Finnish nationalism in mid-1800s, much as a ploy to reduce Swedish influence, and nevertheless the nationalistic trends from Europe reached the Finnish shores as well. Largely as a result, Finnish language had been admitted as official language alongside Swedish, and national-romantic sentiments and literary movement received immense boost from the publication of epic Kalevala poems in mid-1850s. Nationalism had been further hardened by the "russification" program starting from late 1890s: Finnish schoolkids still learn of the "grand petition," a petition, directly to the czar, signed by half a million Finns whereby the russification program of the 1899 "February manifesto" was opposed by "czar's loyal subjects".
Nevertheless, independent Finland very soon faced the greatest crisis in her history as working-class Reds, bolstered by the October Revolution in Russia and angry due to important political reforms being stalled either due to the First World War or due to obstinacy of more conservative politicians, attempted a takeover. In 1918, the Reds and Whites fought a short but exceedingly bloody civil war, which resulted to White victory and, initially, severe repression of the entire left-wing movement, including killings, executions and lethal maltreatment of Red prisoners that had been herded to prison camps - all too often for nothing but a suspicion of subversive activity.
As a result, the challenge for Finnish state in early 1920s was how to build a functioning state from the ashes of the Civil War. The working class was slowly "bought in" by enacting the stalled reforms that had been a major cause of the war, and by increasing prosperity combined with a more lenient approach toward the "reds," even though (or perhaps largely because) the moderate left-wing Social Democrats gained majority from the first post-Civil War parliamentary elections and generally held it since. (Note though that extreme left wing Communists were proscribe.) Meanwhile, education and cultural life emphasized nationalism and drew heavily from the national-romantic themes of the early 1900s, further promoting national unity - although not without drawing considerable criticism, both from the left who saw the culture as being permeated by odious nationalism, and from the right, who saw the culture as being far too permissive of the left-wing "ideologues."
It is still somewhat surprising how well all this worked, and how the Finnish civic society was strong enough to swiftly suppress an attempted right-wing takeover in 1932 - and how the Finnish nation united in 1939 against external, existential threat.
Feel free to follow up if you have any further questions!
Primary source for the above is again Zetterberg's et al's "Suomen historian pikkujättiläinen" (1987).