One thing I neglected in my original response was that I assumed you are using a 5V Arduino. If you are using a 3.3V board then don't connect a 3.7V battery directly.

Assuming a 5V Arduino: Connect Battery - to the GND on the board. Connect Battery + to one end of a 10K resistor and the other end of the resistor to the analog input pin. It doesn't have to be 10K, it can be just about anything from a few hundred ohms to a few hundred K ohms. Use the following formula in your code:

Voltage = 5 * Counts / 1023

If you have a 3.3V Arduino then you need to use a voltage divider to reduce the voltage at the ADC

http://en.wikipedia.org/wiki/Voltage_divider. Connect Battery - to GND on the board and Battery + to 2 resistors in series. The end of the 2 resistors is connected to GND and the middle point is connected to your analog input pin. You want the resistors to be as large as possible because they are going to drain current from the battery. Using two 10K resistors and 3.7V they will draw 185 uA continuously. Depending on the capacity of your battery that could be significant. I recommend resistors between 100K and 500K range. You can calculate what the voltage is at the mid-point using the first formula and the value when you read the analog pin is calculated with the second formula. R1 is assumed to be the resistor between Batt + and the Analog Input and R2 is between the Analog Input and GND:

Voltage(at the pin) = VBatt * R2 / (R1 + R2)

and

ADC Counts = VPin * 1023 / 3.3 <== Replace 3.3 with 5.0 if using 5V system

From those two equations we get the following formula which can be used by your software:

VBatt = (Counts * 3.3 / 1023) * (R1 + R2) / R2 <== Replace 3.3 with 5.0 if using a 5V system

Based on what I've read you probably shouldn't worry about a capacitor. If you have a lot of noise in your system, then adding a capacitor across R2 (from Analog pin to GND) will filter out some of the noise. The formulas for the filter are a little more complicated, so I suggest a 1uF capacitor. If it is still noisy, try 10uF or ask again, telling us your resistor values and how much noise you are getting.