Most breakfasts start earlier than you would like and end before you have warmed up. That is the point: a small room, a short window, and everyone with somewhere to be after.
Arrive ten minutes early
The first ten minutes are the easiest. There are a few people by the coffee, not a full room, and the organiser has time to introduce you. Arrive late and you are walking into conversations that have already started.
If you are new, say so. Organisers would rather know, and most will introduce you to someone.
Have one thing to say
Not a pitch. One line on what you do and who you would like to meet, then ask people about theirs. Curiosity goes a long way.
Leave on time
When the room starts to thin, go. Follow up the same day with one line to the two people you would like to see again.
Go back
The second time is when it starts to work. People recognise you, and the conversations pick up where they left off.