Xibei San Ma
Finland - the basics
Now Finland is a nice country to play. It has some nice tech teams such as FM Mannerheim and Tikkakoski. The downside is that you only have 1 research slot open with your low IC so you should concentrate on Industrial techs early on. Note that your starting infantry is already the 1936 model so your army is in theory already capable to fight. The only problem is that you're a democracy. Elect right in 1936 elections and then change for ministers that improve your infantry building and manpower growth since that's what you're going to need. Do not bother researching tanks. You don't have oil and most of the provinces are forest. The Finnish navy is also near useless so you may want to scrap them although they were fine ships in real life.
Research the doctrines that make your infantry cheaper before actually producing any. If you want to play defensively go ahead and build those damn fortifications in Sortavala, Joensuu and Kajaani but remember that you are building a Greater Finland with its borders in Arkangelsk or whatever.
In 1936 you're just 2 leaps from the "may join alliances" on interventionist slider and since you are in a desparate need for blueprints and such I suggest starting off with this slider. Random events that move you towards authoritarianism are also nice since what you want to do in the following strategy is to be able to wage war before the Winter War :)
You could also move the Democracy slider 2-3 steps, and rule as a dictator, giving you the right to attack anybody.
Finland has a nice surplus of rares. Consider trading this with Germany for energy but remember to have a little extra so you can count on having enough of this after building some factories. You have very good relations with Sweden which is nice because they have some excess metal you also need.
Joining the alliance of Latvia and Estonia can be usefull since you get some blueprints from them and money/resource by trading your tech with them. They get annexed anyway after Molotov-Ribbentrop so why not suck up some juice from them before this?
War with Sweden
If you have had the event that moves your democracy-authoritarian slider by 2 and have made other changes accordingly you will be able to declare war in 1939. The USSR, the UK and Germany have however guaranteed the independence of your neighbours so in order to invade your Scandinavian neighbours you should join the Axis right after their attack in Poland (otherwise this has 0% chance). Invade Sweden! After its annexation you'll have enough IC for another tech team. Germany will help you on this but if you don't restrict their advance without assuming their control they will propably get all the best rare-producing provinces in Skåne (southern Sweden)
The downside is that before you are through with Sweden the Winter War triggers. Give them what they want for now so you can build up your army for the next 1½ years so you'll be ready when Barbarossa starts.
War with Norway
Attacking Sweden without an alliance with Germany usually leads to a highly undesirable war with the axis. Attacking Norway, however, rarely causes any additional wars. Fighting Norway without taking Sweden first is a hard task, considering the fact that you have to attack through the wilderness and mountains of lapland. Norway should be attacked as soon as possible to get more industry.
War with Denmark
In versions 1.0 and 1.1, I always took Denmark. In 1.2 Germany will most of the time declare war if you decide to attack Denmark. If you are allied with Germany, you won't be fast enought to annex Denmark before the Germans. Denmark should be left for the Germans.
Even if you have taken Sweden and Norway, winning the Winter War is impossible without Germany. If you decide to fight and play well, you might push all the way to Archangelsk. Eventually the Soviets will strike back with 100+ divisions and you will lose. Bulding forts is a good tactic, but then the Soviets tend to do a amphibious assault on the western coast of Finland and you are finished. The only advantage you get for fighting the Soviets is that the AI will send ridiculous amounts of divisions to guard the border after the war if you managed to hold on for months, giving the eventual German invasion of Russia an easy task of pushing deep inside Russia. If you accept the Soviet Unions demands, you will have more time to equip your army for the next war and you will not lose manpower.
When Germany declares war on Russia, the fun begins. If you fought well in the Winter War, the border will be swarming with Soviet divisions and you should just defend and wait until the germans are somewhere around Estonia. If you did not fight the Winter War, you should try attacking as soon as the war starts.
Start taking all the provinces you can. You should be extra careful when taking over Murmansk and Kola, as the AI usually strategically redeploys troops to Kola and attacks you from behind. The trip from Murmansk to Kola takes a long time, and probably needs more than one division just in case if a soviet division is redeployed on their way.
You should also try to take Leningrad fast and prevent the enemy from hiding in their forts. You will also need very few divisions to defend Leningrad and you can attack with more power in the east.
You can either try taking the areas of Estonia, or push towards Moscow. Taking Moscow is possible, but getting there before the Germans is hard due to poor infrastructure. Estonia will be easy to get, but Moscow is extremely useful for a small country like Finland. If you managed to take either, start taking all the provinces you can grab. The Germans will eventually pass your troops and you can't take any soviet provinces anymore.
After the Soviet Union and the neighbouring countries have fallen, Finland has very little left to do. It is possible to invade the UK, if you first build giant stacks of subs and get a little lucky. The AI defends the UK very badly, and about 20 divisions will be enought to take Britain. You could also send some divisions to take minor european countries for Germany just to pass time.