I am trying to learn, how to read and use information from an EQ spectrum analyzer, to EQ better. Do anyone have some beginners tips?
in general, use your ears 
Here are a few tips (admittedly more geared toward how to EQ than how to use the spectrum analyzer):
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EQ in the context of the entire mix. In other words, apply EQ while assessing the effect it will have on the instrument in the mix. EQ values may sound great in isolation but could be unusable in the mix (in which case you’d have to re-do them).
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Learn the baisc EQ jobs like rolling off low frequencies to make room for instruments like basses and kick drums, band-pass filtering to make an instrument better sit in the mix, and applying high-frequency shelving to add “air.” However, don’t fall into the trap of relying on so-called “magic frequencies” – use your ears when you EQ (as mentioned above). Each mix is different, even within the same genre.
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Consider EQ-ing with the harmonic structure of the instrument you are EQ-ing in mind. The Cubase EQ spectrum analyzer facilitates this by displaying note values in addition to frequencies.
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Spend time to learn the consequences of applying EQ – i.e., applying filters. The resulting artifacts can be rather harsh/unmusical in some cases.
Something worth doing is to play commercially released recordings through it and watch and listen, eventually you’'ll start to see/hear the correlation between the analyser and what’s being fed through it.
It does take quite some time though… when i got my current interface, which comes with its own metering, i’d very often play commercial recordings and just watch what was going on in conjunction with reading the manual for it.
If i hear a recording i really like now i’ll very often ‘have a look at it’ with the metering too as is does provide one or two clues along with critical listening of course.