Thermocouples are a very common way to measure temperature. They come in a wide variety of forms and have a large range. Do to their small voltage output and something called a cold junction, they are, however, slightly more challenging to read. Most applications need a temperature range of about -50 to +150C, though, and for these applications you might want to consider using a silicon type sensor, as they are cheaper, more accurate and much easier to use. Examples of these are the EI-1022 and EI-1034 sold by LabJack.
Thermocouples are simply two different metals that meet at a single point. Due to a general property of metals, a small voltage is generated that is proportional to the temperature of this junction. There are many different types of thermocouples, identified by a letter such as J type or K type which determine the metals used which then determines the temperature range and voltage output scaling. In all cases, this voltage is between about -5 and 5 millivolts, a rather small voltage.
It gets more complicated though: since the terminals on your DAQ device (the LabJack) are made of yet another metal, there are two more points where different metals are touching which are generating a voltage proportional to the temperature of this terminal. This is called the cold junction. In order to get an accurate thermocouple reading, you have to adjust for the cold junction. This is called cold junction compensation.
Finally, we should mention that most thermocouples are only accurate to about 1 or 2 degrees C, though calibration can help a little with this.
Now that you have the basics down we can talk about how to read a thermocouple. There are several choices depending on what LabJack you have:
U3: the U3 has a resolution of 12 bit and a range of +/-2.44, the minimum voltage you can read is about 1.2 millivolts (4.88 volts / 4096 steps). Because a thermocouple typically outputs around 40 microvolts per degC, you only get a precision of about 30 degrees! Obviously that isn't going to work so you have to use an amplifier such as the LJTIA or EI1040, both available from LabJack, to amplify that millivolt signal before it gets to the converter.
UE9: the UE9 has a resolution of 16 bit so has 65536 steps instead of the 4096 of the U3. This helps some. The UE9 also has some built in gain. Typically you get about 76 microvolts minimum step noise free, and 15 microvolts RMS. This means you get about 1 or 2 degrees C of resolution. This isn't bad and might work. For the exact specs, please review Appendix B of the UE9 Users Guide. If you need better than this, then you will need to get an LJTIA or EI1040 amplifier from LabJack to amplify the thermocouple signal. If you aren't in a rush for your measurements and the temperature is changing slowly, you can also use DAQFactory to oversample by taking multiple measurements and averaging them. This is done by checking the Avg? column of your input channel in the channel table and entering the number of oversample points in the #Avg column.
UE9 Pro: the UE9 Pro gets you an additional 2 bits of resolution over the UE9 (27 microvolts noise free minimum step, 5 microvolts RMS) which is enough to read a thermocouple directly with a reasonable amount of precision. You can use an amplifier as well if you want higher speed readings.
Now that we have that covered lets go over using both methods: unamplified and amplified.