The only thing let me struggle for some minutes was the place for my luggage :hmm:
As I arrived in the morning I had to store my luggage somewhere - I couldn't go to the city with a suitcase at my hand. So I went to the information desk to ask if there are somewhere some baggage lockers. I have to say that it was Terminal 1 where I arrived, and should leave in the evening.
There was a very, very, very "friendly lady" (of course they wasn't) there just telling me "no, no baggage lockers". For the question if there are some in Terminal 2, she said that she doesn't know (I asked myself what kind of persons work at your airport). And she also declined an answer how to come to Terminal 2 too look for myself (I really asked myself what kind of persons there work).
So, with my luggage I got outside, somehow to the bus station at the main street - and yes, the right side to the direction of Terminal 2, as I discovered that it is at the other side of the airport. Without knowing to find something I went to Terminal 2 .... and thankfully, they had a possibility to store baggages.
From there I went with the info given here to the city: Bus to Kispest-Station and Metro to inner city. And in the evening the way back. First to the end to Terminal 2, taking luggage there, going back to Terminal 1 taking flight there. :hmm: Why an easy way, when we can do it on the hard one ....