Well, I suppose your best bet would be to read up on mode 13h programming. The wikipedia page should give you some pointers (pun intended).

See if you can use nasm instead of borland. Borland sucks ass.

Every modern computer comes with the ability to do vesa graphics. If you look in the source code to the old DOS allegro (3.1), you'll see how to use this to set a rather advanced graphics mode (like 320x240x16). Then I'm assuming you use memory mapped io to write directly into the graphics memory.

Be careful that if you're coding in dos without protected mode, you can seriously screw up the system if you "crash" the program. I'd recommend writing this in linux or some other modern OS.

From here on though, I'm not sure how it works. Here's a guess

Assuming the address of a 16-bit framebuffer is 0xA0000
then the instructions to write a white pixel into the first pixel would be (in nasm/intel syntax)

  ;address of fb
  mov ecx, 0xa0000

  ;write 0xffff (16 bits) into first 2 bytes of fb
  mov al, 0xff
  mov [ecx], al
  mov [ecx+1], al

  ;next two bytes
  mov [ecx+2], al
  mov [ecx+3], al

Apparently though its more complicated than that, and you can only write so much at a time. But that should get you started.

one vesa ref:
http://www.delorie.com/djgpp/doc/ug/graphics/vesa.html

Thanks for your answers.
Our teacher said, he wants us to work with mode $03(holy crap...), but I think he wouldn't mind when I choose an other. So, how should I display a space ship, when I can use ASCII only?
We are not allowed to use Turbo Pascal itself, inline assembly only... I mean... we could hack this crap directly into memory...

And...umm... writing stuff into memory is done the same way as writinginto display memory...It was a dumb question, I know...(someone throw a stone at me).

I know how to display ASCII characters, kazzmir. You don't really think our teacher would give us such a killer-task instead of two fucking class tests when we are completely unprepared, do you? Maybe I did not exactly explain what I (and my teacher) want... Okay... I know how to put an 'a' on the screen in text mode $03, but I don't know how to turn this simple 'a' into, say, start ship Enterprise. We will maybe learn how to do it, but I just can't wait a week...

I think what he really wants to know is how to modify the characters in the ASCII table. How an 'a' looks like, how 'b' looks like, how ASCII char 0x12 looks like and so on.
So he can modify the characters themselves and then draw a ship using, say, 4 modified characters.

I know it's possible, but I don't exactly know how.

The only assembly code i've ever done is old Apple II stuff and redcode-94. But here's my advice, based on outdated knowledge:

There's always somewhere in the memory called the screen buffer (500-600 on the Apple II), and there should be a graphics command to change back and forth from ACSII mode to 16 bit pixel mode. Your going to have to find a spot in the mem to define the pixels for your ship, and then have your program your .exe to call that ship to the screen buffer, and switch to 16 bit color mode. I don't know how you would do it on the newer boxes, though. Sorry.