Once you have the
information, write it down!
(Or if possible, record it on audio tape, to preserve the sound itself.)
As you write it, be sure you have the names and dates right. If you have a question, check back with the person who told you about it. If you only have a nickname, find out the full name of the person, and make sure it's spelled right.
Use the same technique for place names. Get the right spelling, and make sure you have the right state (or country)! For example, if a birth or marriage happened in "Marysville", find out which of the dozen or so states that Marysville was in.
And write down the full dates! Don't use the abbreviated "slash" method (like 2/6/45)! Always write the dates in a day-month-year format to avoid any question about their meaning. Write it as 6 February 1945 (or at least 6 Feb 1945). It will save you a great deal of grief later on.
Pictures are important, too. If you have a family gathering, take photographs to remember it by. Then write down the date and place of the photograph, and the names of the people in the picture. When "old" photographs come into your possession, find out as many of these details as possible, and write down them down. Store the details with the photographs so they can be true family heirlooms, rather than just pretty pictures for future generations to wonder at.