Most healing effects in the game require your character to spend a healing surge. You cannot spend a healing surge unless a rule allows you to.
When you spend a surge, unless stated otherwise, you gain your surge value back in hit points. This is usually 1/4 of your total.
A few effects, generally regeneration and a few cleric utility powers, let you heal without spending a surge. Of course, powers that give you temporary hit points are sort of like pre-emptive healing.
All leader classes have a healing ability, which they can use twice per encounter at 1st-level, and three times at much higher level. These are always minor actions, giving the leader a chance to do something for themself, too. The cleric, for instance, has Healing Word, and warlords have Inspiring Word. This lets a PC spend a healing surge, and adds d6 hp to it. (Clerics also have Healer's Lore, a class ability that lets them add their Wisdom bonus to the healing.) A cleric can easily make a healing surge twice as potent, and other leader classes have similar though lesser bonuses.
The cleric's healing strike power, if it hits, lets an ally spend a healing surge.
Healing potions let you spend a healing surge, but give you a set amount of hit points rather than your healing surge value. Basic healing potions give back 10 hp. Generally that's not efficient healing, but it does let you heal as a minor action, and you can stock up on potions if need be, useful for a heated combat when the cleric has run out of Healing Words.
If you run out of healing surges, things get hairy. There's two quick ways of still using your healing surge value.
First, paladins have Lay on Hands, which they can use 1/day per point of Wisdom bonus. This lets the paladin spend their surge to heal another character. It's not as efficient as Healing Word, but paladins get lots of surges so can often afford to spend one or two.
In addition, the cleric has powers like Cure Light Wounds, which let a PC regain hit points equal to their healing surge value without using a surge. Of course, it's a standard action, but if you're out of Healing Words or, worse, surges, and need healing right now, it's useful.
During a short rest, a PC can spend as many surges as they want. It's a little risky, but if you've got a leader, they should be distributing their healing powers at this time. (Yes, you can use encounter powers out of combat, you just need to take a short 5 minute rest to get them back.)
When a PC takes an extended rest, they gain all their surges back. (Unless they've been cursed or something.)
All PCs can use an encounter power, called Second Wind, which lets you spend a healing surge as a standard action and gives a minor defensive bonus. Dwarves get to use Second Wind as a minor action.
Needless to say, Healing Word is a lot better than using a Second Wind. The latter is a last-ditch move of sorts.