user26311: I have a signal that fluctuates between -70mV and 50mV. How would I get the arduino to read this.. Ultimately I am trying to graph the data in real time so it looks like this.

https://imgur.com/a/mZYnErY

user4143: You need to amplify your signal and add 2.5V as a "virtual ground" for the amplification. This gets a little tricky, since you need a low-impedance VCC/2 source to feed the amplifier as a virtual ground.  This would require a unity-gain buffer fed from a voltage divider:

simulate this circuit – Schematic created using CircuitLab
Now you use that to feed the amplifier:

simulate this circuit
The gain is set by 1+(RF/RG), or 11 in this case, giving you -0.77V to +0.55V.
There is a simpler option, though. (There is another intermediate option but the editor lost it and I can't be bothered to spend the time recreating it).
This method does come at a cost, though: it inverts the signal. The -0.07 becomes 0.07 and the 0.05 becomes -0.05, and multiplied by the gain and added to the offset:

simulate this circuit
Here you get a transformation from -0.07V - +0.05V to +0.7V - -0.5V.  That means that in software you then have to invert the value (simply subtract it from 0 after removing the DC offset).
You're basically shifting some of the complexity out of the circuitry and into the software.
Personally I use the inverting amplifier (the last circuit) because the virtual ground current is near zero, so you don't need a low impedance VCC/2 voltage source. It's also easier to create more sensible gains (like 10x) than the non-inverting amplifier, which always has 1 added to the gain.

user7508: Here is my try at this: if your voltage source doesn't mind sinking
something like 150 µA, you could try something like this:

simulate this circuit – Schematic created using CircuitLab
This should map the input range [−70 mV, +50 mV] to
[0.04 V, 4.06 V].

26311: <p>I have a signal that fluctuates between -70mV and 50mV. How would I get the arduino to read this.. Ultimately I am trying to graph the data in real time so it looks like this.</p>

<p><img src="https://imgur.com/a/mZYnErY" alt="Positive/Negative voltage"></p>

<p><a href="https://imgur.com/a/mZYnErY" rel="nofollow noreferrer">https://imgur.com/a/mZYnErY</a></p>
 4143: <p>You need to amplify your signal and add 2.5V as a "virtual ground" for the amplification. This gets a little tricky, since you need a low-impedance V<sub>CC</sub>/2 source to feed the amplifier as a virtual ground.  This would require a unity-gain buffer fed from a voltage divider:</p>



<p><img src="https://i.stack.imgur.com/JUM1h.png" alt="schematic"></p>



<p><sup><a href="/plugins/schematics?image=http%3a%2f%2fi.stack.imgur.com%2fJUM1h.png">simulate this circuit</a> &ndash; Schematic created using <a href="https://www.circuitlab.com/" rel="nofollow">CircuitLab</a></sup></p>

<p>Now you use that to feed the amplifier:</p>



<p><img src="https://i.stack.imgur.com/tgW1D.png" alt="schematic"></p>



<p><sup><a href="/plugins/schematics?image=http%3a%2f%2fi.stack.imgur.com%2ftgW1D.png">simulate this circuit</a></sup></p>

<p>The gain is set by 1+(RF/RG), or 11 in this case, giving you -0.77V to +0.55V.</p>

<p>There is a simpler option, though. (There is another intermediate option but the editor lost it and I can't be bothered to spend the time recreating it).</p>

<p>This method does come at a cost, though: it inverts the signal. The -0.07 becomes 0.07 and the 0.05 becomes -0.05, and multiplied by the gain and added to the offset:</p>



<p><img src="https://i.stack.imgur.com/iElkY.png" alt="schematic"></p>



<p><sup><a href="/plugins/schematics?image=http%3a%2f%2fi.stack.imgur.com%2fiElkY.png">simulate this circuit</a></sup></p>

<p>Here you get a transformation from -0.07V - +0.05V to +0.7V - -0.5V.  That means that <em>in software</em> you then have to invert the value (simply subtract it from 0 after removing the DC offset).</p>

<p>You're basically shifting some of the complexity out of the circuitry and into the software.</p>

<p>Personally I use the inverting amplifier (the last circuit) because the virtual ground current is near zero, so you don't need a low impedance V<sub>CC</sub>/2 voltage source. It's also easier to create more sensible gains (like 10x) than the non-inverting amplifier, which always has 1 added to the gain.</p>
 7508: <p>Here is my try at this: if your voltage source doesn't mind sinking
something like 150&nbsp;µA, you could try something like this:</p>



<p><img src="https://i.stack.imgur.com/fsipE.png" alt="schematic"></p>



<p><sup><a href="/plugins/schematics?image=http%3a%2f%2fi.stack.imgur.com%2ffsipE.png">simulate this circuit</a> &ndash; Schematic created using <a href="https://www.circuitlab.com/" rel="nofollow">CircuitLab</a></sup></p>

<p>This should map the input range [−70&nbsp;mV, +50&nbsp;mV] to
[0.04&nbsp;V, 4.06&nbsp;V].</p>
