Trains in Berlin

Yes you can, but you might not get the best deals.

For buying tickets from Germany this is the "official" website: http://bahn.de
If you use that site above (there is an English version), when you see things such as "Berlin Hbf", it is short for "Hauptbahnhof" which means "Main train station".
There are several train stations from every city. You can use google maps to see if their location is more convenient.

There is a cheaper alternative to trains: car pooling : mitfahrgelegenheit.de

There is a Museum of technology in Berlin. It is not free. http://sdtb.de/English.122.0.html

There is the museum of Military aviation a little outside berlin - it is free. Not to miss if you're interested in this stuff: http://en.wikipedia.org/wiki/Luftwaffenmuseum_der_Bundeswehr
It is on the outskirt of berlin. You will need a zone C ticket. Let me know if you want to go and you need help finding it, because their web presence is utter crap.

Otherwise check out the Tempelhof park which is a former airport which was converted in a huge park. Converted is not the right word... it was basically opened to the public and renamed "Tempelhof Freiheit Park".

I also recommend Burgermeister (but you have a 3/4 hour wait if you go on weekends), and check out the Kottbuser Tör area and it's pubs and bars.

And of course there's the Museum-Insel (Museum Island) which is not free but worth the investment if you're into museums.

I guess your missus and you will love an excursion to Potsdam (zone C, again) , to look at the former imperial palaces there.

That's not "geeky" stuff, but there are a lot of things to see in Berlin, and 3 days is short. I tried to recommend the best stuff.

A zone C ticket is a transport ticket (metro, bus, etc.) that allows you to go far outside Berlin. It is not expensive, but the trip can take 1 hour, or even more, depending on where you start.

Also see if there are any concerts or events you're interested in during that period in Berlin. There are a lot of these happening there.

And oh, of course, there's Checkpoint Charlie and the wall (or Mauerpark), quite touristy stuff but again worth seeing.

There's also Grünewald (a small forest) and the abandoned former american radar station (now covered in graffitis) in the middle of it. Last time I went to that area there were a bunch of Israeli "guides" demanding some payment to visit the abandoned station.

PS: There's a "welcome berlin" card for like 3 or 4 days, it gives you unlimited public transport and substantial reductions on museums and many attractions (with a little book listing them all) - but it's only worth it if you're planning to spend some money on commercial attractions and museums, otherwise 3 or 4 daily tickets will cost less.

Tarek wrotewhere can we buy the zone C ticket ? is there any maps for public transit ?!

Yes there are vending machines in almost any subway station, and they can also be bought from the driver on buses, so you won't have any problem with that.

Maps are displayed in stations, and you can get one at information desks. When you get at the airport, I suggest you to ask for the information desk or anyone who can help you (at the Tegel airport a guy selling tickets at the bus stop helped me). It took me 1/2 hour looking at a gigantic map to find my way to the hostel where I had booked, so ask for directions or prepare your trip beforehand for this first trip to win some time. After that you will figure out how it works. You could also ask random people, Lebanese style, although Germans, in general, are less friendly to strangers than Lebanese.

The authority for public transport in Berlin is called VBB, you can probably find a map online too, although their website is probably not great.

Tarek wrote If I post the train ticket would you tell me if it is for 2 person and if it is ok ?
also if I post my hotel would you tell me how to get to it from tegel airport and how to get to the HBF station from it ?

What did it say when you bought the ticket? I never heard of 2 person tickets anyway (there are group tickets, though).
I could give you the itinerary using Google maps, but I don't really have the force to do it right now - I could do it during the week though.
Your journey will start with a bus, that I can say for sure - there is no U-Bahn (= subway) that reaches Tegel.

Please try to get the name (and line numbers) of the closest subway (U-bahn) stop from your hotel - usually it is on their site somewhere, it will make the process easier - I can then skip finding it using google maps. If your hotel is to the east of Berlin, it might be connected by tram instead of subway, which makes it more complicated.

Regarding Prague to Vienna maybe try to find Czech train company and their website...

Yep, in the upper top right, it says "2 erwachsene", which means "2 adults".
Should have given you my mail or something :)

For the route, try using the route planner on the VBB website:
http://www.vbb.de/en/index.html

In from pick "Flughafen Tegel (airport)" and in the destination type "Wilhelmshavener Str. 71 10551" (make sure to usually add the code because in many cases there will be more than one street with the same name in Berlin) and then put in the estimated time of leaving the airport (like 30 minutes after landing). I've never used it but tested it now and it seems to work. Once you get to your hotel, ask for a subway map from the reception and then you can study it and plan your way around the city, in conjunction to google maps (hope you'll have a good connection). There are also apps you can download to your mobile which can give you routes to take to get to your destination - but you'll need 3G for that...

If you arrive in Berlin in the morning and plan to visit the city on the same day, you might want to buy a daily ticket instead of a single ticket.

I guess your closest u-bahn station is "Turmstrasse".

Mitte is a classy area, but not much happening there, if I remember well.

What are you into and what would you like to see in Berlin

You should be at a 30 minutes walking distance from Tiergarten and a huge Mercedes showroom, among other things.

There is a relatively big zoo in Berlin, BTW if you're interested... but it needs 1/2 day. It's called "Tierpark".

I think your train ticket is valid for one week so if you miss the train don't automatically buy another one! But I'm not sure (maybe you need to cancel 24h before time or something), and in any case try not to miss your reservation. You can ask for more info at any train station there, if you want - my German is far from perfect so I might have missed a couple of details on the ticket, but so far it looks OK.