A writing prompt is a subject to which you write a response. The prompt itself can be a lengthy scene or a single word or phrase. The idea is simply to give you a subject. The prompt is the skeleton onto (and into) which you put the guts and blood and flesh. Writing prompts offer a quick, easy way to begin a writing session, and while you may not use much of what you write in the response to the prompt, you might pen something useful.
In her book on writing, "Bird by Bird," Anne Lamott recommends that writers use note cards to jot down small notes and tidbits of information to use in their writing sessions. She keeps the note cards in the bedroom, in the bathroom, in her car and in her back pocket when she takes the dog for a walk. The idea is that you will always be ready to capture an observation. These quick flashes of insight are easily forgotten, but by writing them down, you will be better able to remember them during your writing session and use them to help the process.
Using your own life experience in writing is an excellent means of getting the process going. Character names, places and events that would otherwise take time to invent can be taken directly from your own life. Even if it is merely a starting point and you change the names and places later, the mere act of beginning the process will move the writing along. While you take the names, places and events from your life, you are in control of what you share, and you can bend those events to meet the needs of the piece.
Free writing is a process of forced, sustained production. Sit down for 15 minutes and start typing. Anything. Just don't stop. The idea behind the process is that you are teaching yourself to produce written language as you would produce speech --- freely, without thought. Even if the end result is wretched, which it usually will be, free writing is valuable because it helps you get something on the page. You can revise later, but get something down first or you will get nowhere.