How to win with a one-province European minor

Quickly ally with somebody much stronger than you are to have protection and try to take some land in his wars
Acquire a second province as quickly as possible, preferably by annexation of another one-province big country
Unite a few small countries if you border with them (easy in Ireland, Italy and HRE, harder if there are none around)
Have good relations with your neighbours and become the Holy Roman Emperor if you are any near the Empire and have monarchy
Become a trading power (invest all your money into Trade research, get an advisor helping in it, take Shrewd Commerce Practice and National Trade Policy national ideas, move with your sliders towards Free Trade).
Keep your stability high to boost your research and tax incomes
Go far in your research of Trade and Goverment
Carefully wait for opportunities and try to take a province with access to sea
Using trading incomes build a colonial empire
Edit your save game, move your capital to the new world and sell your old province to avoid having to defend it

Some interesting little countries:

Navarra - form Spain after starting with just one province and with Aragon and Castille on your back right from the beginning!
Mazovia - squeezed between Poland, Lithuania and Teutonic Order, it is a success to survive till the end of the 15th century
Mantua - unite Italy with the smallest country on the peninsula
Silesia - from a bohemian vassal to the great, holy and roman emperor
Hamburg or Bremen - trade and conquer to unite Germany
The Knights - Conquer and convert all those infidels, control both Judea and Mecca! Deus vult! Dieu le veut! deus lo volt!
Yaroslavl - Do you dare to think you can unite Russia starting with a just one province?