Connect a geophone to an Arduino Uno board
If your ADC handles voltages below ground, then just connect the wires from the geophone to the computer GND and analog Vin.

However, many ADCs only digitize between 0.000 and VREF/VDD.

In that case, create a bias voltage using 2 resistors in series; perhaps 1Kohm or 100 ohm.. 

Then connect the geophone GND/Return wire to the midpoint of the 2 resistors. Insert 1Kohm resistor in series with the geophone "Vout" wire (to limit current in case of huge output voltages), and connect other end of 1Kohm to ADC Vin.

For better performance, place a large capacitor ---- perhaps 100uF ---- from that bias voltage to Ground.

There are much better approaches, using opamps and filtering and bandwidth limitation. But not as simple as I suggest for you to get started. Have fun.

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By the way, you can use a geophone to monitor within your home, to detect outside intruders or inside intruders such as termites. These of course would be above-ground termites.

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instead of amplifying, use a 18 bit ADC, or 20 bit ADC, capable of 50 or 100 conversions per second.  Or 22 bit, if provides fast enough sample rate.

An 18 bit resolution is 256,000 levels. Out of 3.3 volts VREF (assumed), the step size is 3.3uV * 4 == 13 microvolt. The random noise floor should be about 2 to 10 microVolts RMS. Read the datasheets for various ADCs.

Have the top of that 2_resistor voltage divider also connect to the VREF of the ADC.

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what is achievable Random Electron Noise Floor?

Assume 100 Hertz bandwidth, and 240 ohm Rnoise Equivalent in the PreAmplifier.

The total integrated Random Noise, assuming no 1/F noise, will be

2 nanoVoltsRMS/rootHertz * sqrt(100 Hertz) = 20 nanoVolts RMS,

versus a probably 2 microVolts RMS for a high_resolution over_sampling ADC.

But you must implement a shielded box, shielded cables to the sensor, quiet power supplies (no black_brick switching regulators to be used, to prevent any Ground Loops thru the sensor wiring).

You should pose this ----- given assumptions about how many gain_of_4 stages to include before the ADC ---- as a new question.

If you have a QUAD opamp, moderate or low noise internally, and a 4:1 analog mux with one of the QUADS as buffer after the analog mux, you can have

Sensor * 4 * 4 * 4 gain

and use the analog Mux to directly connect to the Sensor, or 4X gain or 16X gain or 64X gain, and add 36 dB dynamic range, plus a reduction of 100:1 in the Random (ignoring 1/F noise spectrum) Noise floor.