Buy a journal or notebook of a convenient size and shape. Make sure it's large enough to write in comfortably but small enough to tuck into a purse or backpack if you will often take it with you. Make sure the journal has acid-free paper if you want to preserve your words indefinitely.
Choose a pen with permanent ink, especially if you are writing a journal for your posterity. Some inks will fade with time.
Determine a regular schedule for writing, if desired, or simply write in the journal when you feel you have something worthy of recording.
Find a quiet place where you will not be interrupted.
Go back and read the last few journal entries - if you have already started your journal - to get you in the spirit of writing again. Notice your moods and emotions as well as the subject matter, and think how they relate to how you are feeling and what you are doing now.
Remember the purpose of your journal before you write. If you are making a historical document, for example, focus on those things of interest historically. Add sketches, quotes and personal experiences as appropriate.
Start writing. Remember that you are not limited to any subject or style (unless you have set those limits based on the kind of journal you are keeping) and that you should include your deepest feelings along with facts and observations. Don't be afraid to let yourself go, and avoid trying to weigh your writing critically in this context.