How to read the Appleman chart to predict contrail formation?
First of all, the Appleman-chart itself:



Source

Now, let's say we want to know if contrails can form at FL340 at my position, a pretty standard cruise flight level. Because flight levels are standard pressure, we can easily look up the pressure, corresponding to the flight level.

100 ............................................ F530 
150 ............................................ F450 
200 ............................................ F390 
250 ............................................ F340 
300 ............................................ F300 
400 ............................................ F240 
500 ............................................ F180 
600 ............................................ F140 
700 ............................................ F100 
850 ............................................ F050 


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Ok, we've got the pressure, it's 250 hPa.

Now we need the temperature at this flight level. I am using a winds aloft chart for this.



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Let's just take a value from what's nearest to my position, -56 degree Celsius in this case.

Now we can look this up on the chart.



Ok, looks like we've got contrails to see. But am I missing something?

I quickly tried to check the result, by looking out of the window. I expected following:


Contrail existing
Very short contrail. I looked up relative humidity for that flight level as well. It's very low, only 3 to 1 percent. And the lower, the humidity, the faster a contrail sublimes and fades away.


Here's the data for the humidity:

-------------------------------------------
PRES   HGHT   TEMP   DWPT   RELH   MIXR   
hPa     m      C      C      %    g/kg    
-------------------------------------------
258.0   9699  -54.9  -79.3    3   0.00 
250.0   9900  -54.3  -80.3    3   0.00   
222.0  10665  -52.1  -82.1    2   0.00   
200.0  11340  -52.9  -83.9    1   0.00   
198.0  11404  -53.0  -84.0    1   0.00  
185.0  11839  -53.4  -84.4    1   0.00  
150.0  13180  -54.7  -85.7    1   0.00  


Source 

So, I first looked on flightradar to search a plane I could possibly spot from my position.



Picture from flightradar24.com

UAE72 is at FL390, what is a standard pressure level of 200, so we've got a relative humidity of 1%.

Now the look out of the window:



As we can see, it's exactly as expected.