Some of the most common fault codes (DTC's) pertain to fuel trim. Here is an explanation of fuel trim and what it does for us.
The ECU controls Air/Fuel mixture in order to maintain power, efficiency, and emissions. A/F is expressed as either a ratio (14.7:1 for example) or as a Lambda value. With iso-octane ("ideal" gasoline), Lambda of 1.0 is equal to 14.7:1 A/F. This is known as "Stoichiometric", a condition where there is a perfect balance between oxygen molecules and the various hydrogen and carbon based molecules in petroleum. With the oxygenated gasoline that most of us use, actual A/F ratio of 15:1 is closer to stoichiometric.
If Lambda is greater than 1.0, then there is a surplus of air and the engine is running lean. If Lambda is less than 1.0, then there is a surplus of fuel and the engine is running rich. It should be noted that the ratios are mass-based, not volume-based.
So, why don't we always run at 1.0 all the time? Well, we do MOST of the time. At cruise and idle, mixture is held tightly to 1.0 to keep the catalytic convertor at optimal efficiency, so the emissions are minimized. However, when we need acceleration, the mixture gets richer. Why? Maximum power is made between 0.85 to 0.95 Lambda (12.5 to 14.0 A/F with iso-octane). So, under acceleration, mixtures get richer. Sometimes you want to get even richer under acceleration to keep detonation (pre-ignition of the mixture from excess cylinder temperatures) away. The 1.8T, for example, has a relatively high compression ratio for a turbocharged engine, which especially under lots of boost, is very succeptible to detonation).
So, now that we know that the ECU wants to be able to control the A/F ratio. It has a prescribed set of values (maps) for a given RPM, Load, etc. So, the ECU tells the injectors to pulse for exactly XX.X milliseconds and that SHOULD get us the proper A/F ratio that we want. Well, if you tell an employee to go do something, you want to make sure they actually did it, right? The ECU has some snitches (the front O2 sensor and the MAF, for the most part) that will report back whether or not the desired mixture has been attained. The rear O2 sensor is used mostly to monitor the condition of the catalytic convertor, although in some applications it also contributes to trim information.
Based on feedback from the snitches, the ECU learns to apply a correction factor to its commands to the fuel injectors. If you know that your employees take longer than the standard allotted time to do a specified job, you will need to adjust for that in your planning (injectors are in a union, so it is tough to fire them ). The learned values go between the maps in the ECU's Flash ROM (the "chip") and the signal to the fuel injectors. These learned compensations are known as "trim". So, when you see "trim", it means "compensation".
"Add" means additive trim, which is addressing an imbalance at idle. When the ECU is using additive trim, it is telling the injectors to stay open a fixed amount longer or shorter. The malfunction (e.g. vacuum leak) becomes less significant as RPM increase. For additive adaptation values, the injection timing is changed by a fixed amount. This value is not dependent on the basic injection timing.
"Mult" mean multiplicative trim, which is addressing an imbalance at all engine speeds. The malfunction (e.g. clogged injector) becomes more severe at increased RPM. For multiplicative adaptation values, there is a percentage change in injection timing. This change is dependent on the basic injection timing.
You can check your current state of trim by using VAG-COM or equivalent to look in Group 032 in your engine measuring blocks. The first two fields will have percentages. The first field tells the fuel trim at idle (Additive). The second field tells the fuel trim at elevated engine speeds (Multiplicative). Negative values indicate that the engine is running too rich and oxygen sensor control is therefore making it more lean by reducing the amount of time that the injectors are open. Positive values indicate that the engine is running too lean and oxygen sensor control is therefore making it richer by increasing the amount of time that the injectors are open.
It is totally normal for both the first and second fields to be something other than zero. In fact, zeros indicate either you just cleared codes (which will reset fuel trim values) or something isn't working properly. If values get too far away from zero, it will cause a DTC (fault code) and can set off the MIL (commonly referred to as the Check Engine Light, or CEL).
Specifications for normal operation are usually somewhere near +/- 10%.
In general, an out-of-spec value in the first field (Additive) indicates a vacuum leak since it is mostly present at idle, when vacuum is highest. An out-of-spec value in the second field (Multiplicative) indicates a fault at higher RPM, and may point to a faulty MAF.
Here's a good sanity check for the status of your MAF. Do a full-throttle run all the way to redline in a single gear (second works fine). Group 002 usually shows air mass in g/s. Your peak airflow should be roughly 0.80 times your horsepower. So, if you have a stock 150 hp 1.8T, expect around 120 g/s. If you have a 201 hp 24V VR6, expect around 160 g/s. If you see significantly less than that, you MAF may be on the way out. This still works if you are chipped, but "race" programs may make more power through timing, rather than airflow. Therefore, take all readings with a grain of salt.