Hello everybody. I have arduino duemilanove, bipolar stepper motor with 4 output wires and H-bridge that I made on a breadboard with 4 NPNs. Could somebody please explain me how could I, using things that i have, at least make this motor move.
It may not even be possible, with what you have. Post a complete description of the parts and a circuit diagram.
Stepper motor is from an old floppy drive and the only thing that is written on it is 3825C1146 and it has 4 pins. I don't know how to make circuit diagram "sketch" on PC, but I have made H-bridge on breadboard with 4 NPNs and 4 diodes and 4 * 10k ohm resistor which are controling base current and I'm controling transistor over pins 3, 9, 10, 11.
You need to do a bit of googling. Evidently, you are unaware that you need two H-bridges to control a four wire stepper motor. Furthermore it is extremely difficult to build a functioning H-bridge with only NPN transistors. Usually, two PNP transistors are used in addition to the NPN transistors.
As for asking questions of the forum, here are a couple of starters:
There are tens of thousands of different types of NPN transistors. Which ones do you have?
Without a schematic or a clear photo of your setup, how are we supposed to know that you wired everything correctly? If you don't know how to draw a schematic, follow one that you find online exactly, and give a link to it.
What is the resistance of the motor coils?
Hi, you can draw a circuit diagram and photograph it, if you have those facilities, a phone camera can do a great job of copying from A4 sized paper.
But I agree with previous posts, NPN to make a H bridge is hard to visualise, also you will need to power the stepper motor separately to the arduino.
Tom..... hope to get you on the right track .. 
Save yourself all the headaches and get a stepper controller breakout board:
If you just want to get started with steppers this is the cheapest alternative and surprizingly effective provided you do not need high speed.
5-wire unipolar 28BYJ-48 with ULN2003
I got myself L293NE (http://datasheet.octopart.com/L293NE-Texas-Instruments-datasheet-8627554.pdf), but i don't know how to connect it all together. Could anyone give me some advice?
I got myself L293NE
Go ahead and use it if you must. You should understand that true stepper controllers are much more effective with 2 phase motors, providing both improved microstepping and better torque.