I would say begin with the touristy stuff. You'll want to buy a BVG Tageskarte (day ticket for all local transportation). A Zone A/B ticket should suffice unless you want to go out to Potsdam. If you do that, you'll need a B/C or ABC card as well. These run 6,50 € to 7,00 €, respectively. You can use these for any U- or S-Bahn, tram, or bus. The ABC card may also be good to use on certain local RE trains but be careful.
I would start at the Alex or Alexanderplatz and walk west along Karl-Liebknecht Straße and then to famous Unter den Linden. (Walking further east a few blocks on Karl-Liebknecht will take you to Hofbräu Berlin. But keep in mind that the place is for tourists as Bavarian culture does not apply to Berliner culture.)
Things to see along the way...
1. Die Weltzeituhr (am Alex) (World Clock)
2. Fernsehturm (TV Tower)...costs a lot to go up but the views are great.
3. Neptunbrunnen
4. DDR Museum (optional...will mention more later)
5. Berliner Dom
6. Museum Island (esp. the Neues Museum and the Pergamon)
7. Deutsches Historisches Museum
8. Neue Wache
9. Cross the street to Babelplatz (visit the Denkmal zur Bücherverbrennung am 10. Mai 1933)
10. Keep walking south behind Babelplatz and visit Gendarmenmarkt.
11. Buy some Rittersport chocolate at BunteSchokoWelt (Französische Straße 24)
12. Continue walking west to Friedrichstraße then walk back north to Unter den Linden and then west again to the Brandenburg Gate.
13. Walk south to the nearby Memorial to the Murdered Jews of Europe. If you walk southeast of the Memorial along Getrud-Kolmar-Straße, you'll see the site of the Hitlerbunker. Continue walking south you'll come to the famous Potsdamer Platz (looks like a giant tent in the shape of Mount Fuji).
14. Walk north to see the Bundestag/Kanzleramt/Berlin Hbf Main Train Station.
15. If you have the time/energy, continue walking west along Straße des 17. Juni (or even better through the Tiergarten) to the Siegessäule.
Now doing the above on foot minus the museum visits #6 and #7 would take you 3-5 hours probably. Each of the museum visits in bold above requires a minimum 2 hour stay.
The above just details the main touristy route through the heart of Berlin. My next reply will have a few additional recommendations for more specific themes.