Several stays: many-to-many relationship Could you please help me with the following problem? I'm a total novice in DB design. 

I have a table with researchers who visit our university. They come for some period of time (from, till). Now, how can I save in the database if somebody came several times? I have an entry already for a particular person and need to add some other stays and be able to see them in a form. 

My idea was: this must be a many-to-many relationship. Ok. Then I need a third table Researcher/Stay. And then I don't know what to do next. In Stay-table "from+till" is a key. I haven't seen examples with double-value key in a many-to-many relationship and don't know what to do next.
Based on your diagram above what you have is a one to many, not a many to many relationship.  You have your Researcher table and your Stay table.  If you add the researcher id in the stay table to the primary key you have a relationship of:

Researcher.ResearcherId -> Stay.ResearcherId 

Where a given researcher can have multiple stays.  For example

Researcher John Smith has an Id of 2.

In the stay table you would have

From       Till       ResearcherId
1/1/2013   1/5/2013   2
2/6/2013   3/1/2013   2


etc