Next Alex says that the secretary will type up a list.

"To type up something" means to take information that someone has written on a piece of paper and put it on a computer - to type it in, or to enter it into a computer.

Sometimes it is difficult to type up other people's notes and comments because it is difficult to read their handwriting.

"Handwriting" is what you put on a piece of paper with your hand: letters and numbers and so forth.

The secretary is going to type up a list of everyone's contact information.

Your "contact (contact) information" is your address, your email, your telephone number, perhaps your fax number, any information that can be used to communicate with you - to, we would say "get in touch with," to communicate with you, to get in touch with you.

Many websites, for example, ask you to provide your contact information.

Alex, in the meeting, is asking people for their contact information so that he will know how to communicate with them and they can communicate with each other.