When choosing to write in the third person most of us will choose to write in the Third person omniscient form which is the most popular form of third person writing.
However, when writing in third person you do have other options. As well as Third Person Omniscient you also have the choice of Third Person Objective or Third Person Limited. I will explain the differences and talk about each form.
When writing in third person we are telling the readers what our characters are doing and, depending on which third person form we're writing in, reading their thoughts. In first person we would use the words I did, but in third person we only ever say he or she did.
Third person omniscient
In third person we can follow each of our characters and watch all their actions. However we write differently depending on which form of third person writing we are using. The most common, and the one I personally find easiest, is the third person omniscient form.
When writing in third person omniscient we use the words he and she. She said'; he thought'
E.g. Angie looked around the strange room. Where am I?' she said.
In third person Omniscient we show can the thoughts and actions of all our characters.
E.g. Paul felt tears well up in his eyes as he put his arms around her and held her tight. "I'm here," he said. "You're safe now."
Third person limited
Third Person Limited is similar to the Omniscient form, but here we are limited to the thoughts and actions of just one character. In this way it helps the reader to emotionally connect with that character. We are only listening to his/her thoughts and are thereby drawn closer to that character.
Other characters may be in the scene, but it's only the thoughts of our main character that we learn about. It's only his/her thoughts that the reader will care about.
E.g: Laura stared at him. "I'll tell them everything I know," she shouted. She said it to call his bluff, but in truth she knew she'd do anything to get him out of her life.
She looked at the sneer on Paul's face. "You just try it," he said. She thought for a moment he was going to hit her, but he turned and walked away.
Third person objective
When we write in the Third Person Objective we are only writing about our character's actions and not his or her thoughts. Here we do not use, he said, or she said. The reader isn't told what is going on in the character's mind, but should be able to work this out from what the reader is doing or what is happening to him/her. In other words, it is up to the reader to decide what is happening in the character's mind.
E.g. She laughed as she ran across the soft sand and felt it's warmth on her feet. He was close behind her and it wasn't long before he caught up. His strong hands took hold of her and pulled her down into the sand. He ran his hand gently over her skin and they lay there together for a few moments under the hot sun.
He reached over and stroked her hair and pulled her head towards his. As their lips brushed lightly together, she laughed and jumping up, ran towards the water. From the water's edge she looked around to see if he was in pursuit, but he was just sitting there, watching her, with a smile on his face.
As you can see from these two paragraphs we have not told the reader any of the character's thoughts, only their actions. From this we can tell that the characters are lovers and by female character's actions we can tell she is teasing him.
These same paragraphs could be written in such a way that the female character could be trying to escape from the man and doesn't want his attentions and we could still tell this without describing their thoughts.
That is a brief summary of the different ways you can write in third person. Try them all and see which one you prefer and have fun.