By using a noun or a phrase in apposition

Mr. Paul is my tenant. He doesn’t pay the rent regularly.
Mr. Paul, my tenant, doesn’t pay the rent regularly.

Rama killed Ravana. Ravana was the king of Lanka.
Rama killed Ravana, king of Lanka.

Alice is my girlfriend. She is Spanish.
Alice, my girlfriend, is Spanish.

He won the first prize in singing, dancing and acting. It was a glorious performance.
He won the first prize in singing, dancing and acting – a glorious performance.

By using a preposition + noun/gerund

She has a lot of money. But she is unhappy.
In spite of having a lot of money she is unhappy.

He was a good writer. He was also a good orator.
Besides being a good writer, he was also a good orator.

He had a great deal of influence. But he could not get the award.
With all his influence he could not get the award.

By using an adverb or an adverbial phrase

Two simple sentences can be joined into one large simple sentence by using an adverb or an adverbial phrase.

They will come. That is certain.
They will certainly come.

They decided to elect John their chairman. All agreed to this.
They unanimously decided to elect John their chairman. OR By common consent they decided to elect John their chairman.

Exercise

Combine each of the following pairs of sentences into a simple sentence

1.    He won a jackpot. He built a big mansion.
2.    He stood on tip-toe. He reached for the bunch of grapes.
3.    He is going to London. He wants to pursue higher education there.
4.    Milton was the Homer of England. He wrote Paradise Lost.
5.    Patel was a strong man. He brought all the Princely States into the Indian Union. He used the method of persuasion. Sometimes he used the method of coercion.
6.    Gandhi was a great visionary. He realized the danger of communal conflicts. He sacrificed his life to bring about unity.

Answers

1.    Having won a jackpot he built a big mansion.
2.    Standing on tip-toe he reached for the bunch of grapes.
3.    He is going to London to pursue higher education
4.    Milton, the Homer of England, wrote Paradise Lost.
5.    Using the methods of persuasion and coercion Patel, a strong man, brought all the Princely States into the Indian Union.
6.    Having realized the danger of communal conflicts Gandhi, a great visionary, sacrificed his life to bring about unity.