Both these methods are especially suitable for cooking vegetables, though the can be used for some meat dishes.Both are water-based, which means no fat is needed. This makes them both potentially healthy methods; "potentially" because if you boil or steam food for too long it loses its nutrients. Steaming does have some advantages: it loses fewer nutrients than boiling, and if you do leave food in for too long it still tastes good, whereas overboiled food is completely tasteless. On the other hand, it takes longer and you need slightly more equipment.
For boiling you just need a saucepan. For steaming, you can use one pan inside another (the food mustn't get water on it), but it's more efficient to get a special steamer. The old-fashioned Chinese-style steaming baskets work perfectly well; just get a pan of boiling water and stand the basket inside. Even simpler is the electric steamer. This is filled with water in the base; the food is put in containers above it, and you just switch on. (one tip: most vegetables taste great from a steamer, but potatoes can be quite slow and need to go in early.)
For boiling you just need a saucepan. For steaming, you can use one pan inside another (the food mustn't get water on it), but it's more efficient to get a special steamer. The old-fashioned Chinese-style steaming baskets work perfectly well; just get a pan of boiling water and stand the basket inside. Even simpler is the electric steamer. This is filled with water in the base; the food is put in containers above it, and you just switch on. (one tip: most vegetables taste great from a steamer, but potatoes can be quite slow and need to go in early.)