A marathon is altogether different league when compared to a 10 km run. There are many things to consider...
You should have a proper hydration plan in your long distance races. For 10 km races, you wouldn't probably have had hydration during the race course. In a marathon, I would advice you to start hydrating from the 5 km mark. From there on, every 2 or 2.5 km you are adviced to hydrate alternatively with electrolytes and water and if possible with energy gels (or other energy substances).
Long distance training
As you say, you have run many 10 km race, you would have good stamina but that need not be as good enough for a full or even a half marathon. Start running the weekend long end runs. During the weekend long runs, keep it very slow. Go for some 32 km runs at a very slow jolly pace. The idea is to keep many strides than the original race or at least equivalent to that. So, the stride length should be very less. This allows your joints to get ready for a full marathon. Also this improves blood flow.
If you are interested in improving speed, go for intervals (once per week). My favorite is Emil Zatopek's way of training. Run 400 m fast runs with rests in between. Warm-up before the intervals and cool down after the intervals are very much important. The interval training helps you reduce the resting heart rate, which is very important for long distance runs.
Get your muscles ready for the long run. Go for calisthenics during most of the strength training and also weight training once in a week. Also try resistance training for your thighs like running on the sand or pulling something while running, etc.
Prepare your mind
The marathon is not a race in your initial stages. Make friends with runners, run with groups, enjoy your runs. More importantly, put a smile on your face while running. Most importantly, thank the volunteers while running a marathon.
My understanding on heart rate and interval training:
Resting heart rate is calculated by counting the pulse rate or heart rate after you lie down for half hour or so. Your maximum heart rate is approximately 220 - age. The difference between max and resting heart rate is taken as diff for further calculations.
Generally long runs are run at a heart rate between 50 to 60% (resting heart rate + 50-60% of diff)comfortably. If the this percent is close to the max heart rate then the person will get tired soon. So the resting rate is to be reduced in order to reach greater speeds with ease, for long runs.
For a normal man the resting heart rate is 72 bpm (beats per min). In order to reduce the resting heart rate, one does interval training, during which the heart rate is pushed close to the max heart rate (or held near the threshold limit for a long time) while sprinting (fast runs) and reduced to very low rate (as low as possible) during the resting period (or slow jog). This kind of subsequent peaking and reducing heart rate, results in lot of fat burning and over course of time reduces the resting heart rate.
Thus the above method of intervals reduces resting heart rate and allows us to run fast for a long period of time (distance).