Q:

How to read a push-pull output

I recently came across a sensor that had a "push-pull" output. I can't find anywhere how to read such an output:

Is it some particular kind of analog output?
I would want to read it with the MSP430G2553 (using energia or code composer).

A:

A Push-Pull output is your normal CMOS or TTL-like output.  It's either HIGH (IO pin is connected to VCC through a MOSFET), or LOW (IO pin is connected to GND through a MOSFET).
The basic circuit of the output stage is as simple as:

simulate this circuit – Schematic created using CircuitLab
It is the technical name for any "normal" digital output pin, and can be connected direct to any normal digital input pin that expects to work with the same voltage ranges.
That is as opposed to an Open Drain (or Open Collector) output which basically omits the P-channel MOSFET and just switches the ground connection on and off (these require a pull-up resistor or other similar setup to work).
Also, push-pull outputs are also used in the analog domain where they are effectively an amplifier. It uses the same arrangement - a high and a low transistor of some form, but it operates in the linear, not the saturation region of the transistors.  This mirrors the incoming waveform with more power.
If your sensor is of the analog type, then it will provide a simple analog signal out of it, amplified by the push-pull amplification stage.  This output can be connected direct to any analog input pin that expects to work in the same voltage range.
Simplified push-pull amplifier:

-- Wikipedia
It is called push-pull because the top transistor pushes power out of the pin from Vcc, and the lower one pulls the power in from the pin to ground.

A:

Just connect it - and only it - to the MSP device pin.
A "push pull" output is one that can't be shared with other outputs (to save I/O pins) and doesn't need a pull-up or pull-down resistor. Which makes it the easiest sort to use.
An "open collector" (or "open drain") output can only pull the voltage down to 0V, but not up to +V. This means it can be connected to other outputs of the same type without damage, but needs a "pull up" resistor to signal '1' when it is turned off. (The MSP430 has these pullups built in, there is a special register to turn them on or off)

A:

push-pull is the name given to a "totem-pole" style of output driver, commonly seen in micro controller/digital outputs. The "push" stage is when the output is logic high, and a transistor sources current from VCC and "pushes" it out into the output. 
The "pull" stage is another transistor, which pulls the output to ground.
These are often used as MOSFET drivers too, because they can sink and source large amounts of current, rather than an open collector with (internal or external) pull up resistor which is another common alternative (these are only strong to "pull" or sink current, cannot provide much current).
If the transistors are CMOS fets, they will be basically VCC or 0V. If they are older style PNP/NPN drivers, sometimes using Darlington pairs for higher current output, they may not provide the full VCC output voltage (close to it though!) and may not reach 0V on the "low" output either, usually less than 1V though. 
EDIT: to answer the "analogue output" specific part of the question, The output will be related to the sensor reading or whatever internally is happening, and in addition to a normal push/pull style output there will be a feedback associated which allows the "set point" of the push/pull output to drive properly, over an external or internal (read the datasheet!!) load resistance. See the image below for how it may be done on your device.

