The best foods, in my experience, are oily fish (especially mackerel, but also sardines, salmon and tuna) and seeds (especially flaxseeds, pumpkin seeds and sunflower seeds, all of which you can sprinkle on bread, add to salads, rice and other dishes or just eat straight out of the pack), plus fresh fruit and vegetables of every colour of the rainbow.  Dark, leafy green vegetables like broccoli, cabbage, calabrese, spinach and spring greens are especially effective; be sure to steam them lightly (spinach can also be eaten raw, in a salad with rocket and watercress) so as not to get rid of all of the nutrients!  Red peppers for some reason also seem to have a great effect.

Replace your cooking oils and fats with olive oil (which you can use as a butter/margarine substitute on bread too) or flaxseed oil.

Cut out alcohol, caffeine and refined sugar.

Drink at least 3 litres of water per day (tap water is fine - buy a cheap filter and keep it in the fridge, if you don't like the taste of it straight out of the tap).

Lastly, some people find that dairy products affect their skin negatively, so you may find that cutting out or reducing them in your diet gives you a healthier scalp.  Dairy products can be good for other parts of your overall health, though, so think carefully (and maybe consult a doctor) before cutting them out completely.  They're a great source of calcium that strengthens your bones and helps to ward off osteoporosis.

Good luck - hope this helps.

Sorry, I forgot the most important one of all: SEAWEED.  You can buy it toasted in sheets (a bit like crackers) and although it has a bizarre taste, it's not unpleasant.  I always think it tastes a bit like rice crackers.  It's absolutely brilliant for your hair, though.  Try a health food store, as I've never seen it in a supermarket.

Dried fruit (without added sugar), especially apricots, work well for me too.