It's quite easy to read data off of magnetic stripe cards. Each card has up to 3 horizontal tracks of data (but the third track is rarely used). Track 1 is formatted according to IANA standards, which means 7 bits per character. Individual bits of the digital data are physically stored using Aiken-Biphase encoding, which means a 0-bit is represented by a zone with a single direction of magnetic flux, and a 1-bit is represented by a zone of two different magnetic flux directions. This can be visualized using < and > characters representing the different directions of magnetic flux:
This represents the bit pattern 00001010. A magnetic field acts like a flowing river of water, and at the center of a junction like >><< the two waves collide, which causes the magnetic flux density to grow very high around that point. Similarly at a <<>> junction, the magnetic flux at the middle point becomes very strong but with the opposite polarity than the >><< junction. We can detect this magnetic flux polarity by moving a coil of wire through the magnetic fields that surround the magnetic zones. As the coil moves through the field, the changing magnetic field strength causes electric potential in the coil. If the coil is hooked up to an electric circuit, it will act like an AC generator, which switches polarity whenever the coil passes from one zone of magnetic flux to a zone of the opposite magnetic flux. Spikes of electric potential will be induced in the coil as it passes the >><< and <<>> junction points. We can analyze the timing of these spikes to recreate the original data stored on the magnetic stripe.
I salvaged the tape read head from an old audio cassette player. Tape heads are just a small coil of wire mounted in a chunk of plastic or metal. The coil in the tape head was connected to 4 individual wires, and I used a multimeter and found that 2 pairs of wires had 300 ohms of resistance between them, and the other wires weren't electrically connected at all. I guess this is because the tape head has 2 separate coils to read stereo audio tapes. I cut an old audio cable in half and connected the GND and LEFT wires to one of the coils in the tape head. I plugged the audio cable into my sound card's Mic input, and turned up the amplification of the Mic channel. I swiped the tape head past a magnetic stripe and I could hear a garbled digital chirp. I used Audacity to record the chirp and zoomed in until I could see the waveform clearly. Sure enough, the areas where two opposite magnetic fields collided could be clearly seen as positive and negative spikes in the signal.
According to ISO standard 7813, track 1 (the topmost 1/3 of a magnetic stripe) is padded with 000...000 at both ends so it's easier to parse the data. At the default zoom level, I found that a pencil fit perfectly inside the width of a single bit. Then as I moved the pencil along the signal, 0-bits were represented by the signal changing state once along the pencil's width, and 1-bits were represented by the signal changing state twice within the same timeframe. Using the pencil trick, I managed to read the entire sequence of bits for track 1 of my credit card. Then I grouped them into 7-bit chunks, and looked them up in the ISO 7813 character table. Using this method I managed to read all of the stored information off of the credit card. In the waveform below you can also see that I didn't swipe the card at a constant speed, so the leftmost bits are spaced slightly wider than the rightmost bits, but it's still very easy to distinguish the data.