“Know how to listen, and you will profit even from those who talk badly.”
Plutarch
Be interested in subjects that are not immediately yours:
In the early stages, it is difficult to relate to distant topics outside of our immediate research problem. But this is a crucial step on acquiring a broad view of the area. One needs to know different problems and have a feeling of the different techniques available. Also it is important to know who is doing research in what.
Attend talks and conferences, even those not directly related to your work
(Terence Tao)
Take notes:
There is something about taking notes that really help us getting into the subject matter of the talk. You don't need to write down everything. Be selective and try to keep a space for the questions you might ask later
https://mathoverflow.net/questions/12638/taking-lecture-notes-in-lectures
Don't try to follow every step:
Usually in seminars, talks are very dense. The speaker wants to give a feeling of the interesting problems of his area. For us in the audience, less familiar with the subject, and not having the definitions so ready in mind, it is very easy to drift of at some cumbersome passages. If that happened to you you can try to go back to the big picture. Ask questions about and focus on basic main ideas and motivation that might help you get back on track of the talk.
The "Three Things" Exercise for getting things out of talks
(Ravi Vakil)
Read ahead:
Reading about the subject matter before the talk, even for about 15 minutes is already of great help. You will get to the talk with some ideas of the problem and the talk you be more easily understandable.
Look for connections:
The topics in research are recurrent. When you are seeing a talk, you can probably relate its content either with your research or with other talks. In this way you can keep a constant update of what your are learning in talks, and this will probably serve you later in your own research.
Ask Questions:
Remember what you learned:
A talk should not be immediately forgotten at the moment of its end. Try to keep your notes of the talks so that you can go over what was exposed. Spaced your repetition of the content in time and you will have a better sedimentation of the content of the talks
Further reading:
(T. W. Korner)