Most Analyzer Techs will start off as Instrument Techs and you must have a basic understanding of instrumentation to do analyzer work.

It doesnt matter whether you work in a refinery or a chemical plant, they will use the big 4 to control the process.
                       FLOW - LEVEL - TEMPERATURE - PRESSURE
There are tons of other variables that will be measured depending on the process such as pH, conductivity, RVP and so on but the big 4 are the main PV's (process variable) we use to control.
    You must learn the basics in how the transmitters send the data to the DCS. Once you understand analog signals you will be ahead of the game. As we advance with communications and the price of wire continues to rise we are seeing more and more signals being sent through fiber and such. You will hear terms like mod bus, TCP/IP, RS 485 and so on. It takes time to understand the communication part but normally once it is up and set you will not have to go back into this in the future.
Flows are so critical to the process. Lets think about a batch process and you have to feed this much of this and this much of that and mix it and heat it up to this in order to create our end product. If you'r ingrediant amount is off, then we don't make good product and have to throw it away and start over.
Flows are measured numerous ways. I think the most common method is with a DP transmitter coming off an orifice plate. A DP is a differential pressure. A common practice now days is for the engineer to make the orifice hole to the size that will give our transmitter an easy range of 0 to 100"H2O.
Other ways to measure flow are mag meters, coriolis meters, ultrasonic, and mass flow using temperature and pressure compensation.
Levels - when I first started in this field were tip tubes and displacers and DP transmitters with capillary paddles mounted right to the tank.
Now days we are seeing more and more guided wave radar levels or ultrasonic level transmitters. Depending on the vessel or tank or whatever you are trying to measure will determine what type of level transmitter you will use.
Levels are easy but I say again that you must learn the basics such as 27.7" H2O = 1 PSI = 2.04" HG and that 8.337 lbs = 1 gallon of water and all that other math for just figuring out how much volume is in the tank and so on.
At my current plant there are weight scales on the edges of tanks and they determine the level by weight.
Pressure is simple and your main problem with doing them is finding the right hand pump and crystal to go up that high. Also make sure you carry plenty of reducing fittings such as 1/2" to 1/4" and 3/8" to 1/4"..... When does pressure get confusing? When you have to do a vacuum transmitter and the range is 0 to 1600 mmHg. I will not write this all out on here but your transmitter will be around 50% output sitting on the bench. Pull a vacuum of 760 mmHg =30"Hg and get your 4ma = 0% then apply positive pressure of 840 mmHg to achieve your 20ma = 100%

If you don't understand that it's OK. A lot of senior technicians don't get it either.
Temperature = Know your thermocouple colors and some of the wires that make them up. The most commonly used TE's ( temperature element )are J, K, & E and I would say 95% consist of J and K. J will come in a black covering and the wire colors are red and white. Red is always negative on a TE. Say that about a hundred times cause you need to know that. The wires that make up a J thermocouple are iron & constantan. A type K has a yellow jacket and the wire colors are yellow and red. RED IS ALWAYS NEGATIVE. The wires metal consists of chromel and alumel.

Somebody figured out a long time ago that if you twist two dissimalar metals together that they produce and EMF ( electromotive force ) read out in millivolts. These millivolts can be measured and from there we can derive the temperature. The more heat that is applied the more millivolts you will get. ​​
​RTD - resistance temperature device. Typically a three wire setup but it can be two wires or four wires. An ohm value is produced and from this ohm value we can determine the temperature. The most common one I have seen is the 3 wire 100 ohm platinum. Two wires will be the same color - red and the other will be different - white. If you were to measure with your meter from red to red you would have a dead short. Read from one red to white and you will have an ohm value and if you measure from the other red to that white you will see the same ohm value. Remember this also. if you measure it at ambient temperature and that ambient temperature is around 75 degrees ------ you will read 109 ohms. As temperature goes up. So does resistance.