If I remember correctly, the main sights are close to each other

If you don't plan on entering a lot of museums, you can cover a lot of ground in a day or two. You can take trams, buses, or the metro.
It's been three years since I've been there and I still remember a lot of things, even the Czech names! Some other stuff in bullets--
- I find the Green Line metro stations (I'm assuming it's the most 'touristy' line) fascinating
- The Czechs have the highest per capita beer consumption in the world

Try pub hopping if you are into that sort of thing. The draft beer (e.g. Pilsner Urquell) is really good and the country is known for their good beers
- Restaurants within the vicinity of Staromestske Namesti (Old Town Square) are touristy / expensive. Learned that the hard way
- If you're Catholic, do visit the church of Sto. Nino de Praga / Prazske Jesulatko. I believe it's popular among Filipinos as a pilgrimage site
- Good day trips from Prague: Cesky Krumlov and Kutna Hora. How long will you be here for? If you have a lot of time you can visit Vienna or Budapest, equally beautiful cities in their own right
- Good souvenirs: matryoshka (Russian nesting dolls), Bohemia Crystals
- Some "essentials": Prague Castle, St. Vitus Cathedral, Petrin Hill / Tower, Staromestske Namesti (Main Square), Charles Bridge, Tyn Church, Vrtbovska Zahrada (Vrtba Gardens), Lennon Wall, Jewish Cemetery, Orloj (Astronomical Clock), Tancici Dum (Dancing Building), Wenceslas Square (a lot of nice shops)
- Currency is Cesky korunas (Kc)