Here are the verbs in the present progressive:

1) is celebrating
2) is having
3) is not raining
4) is shining
5) are waiting
6) are wearing
7) is smiling

So the completed sentences would be:

Elaine **is celebrating** her birthday today and she **is having** a party in the backyard. It **is not raining** and the sun **is shining**. All her friends **are waiting** for Elaine to blow out the candles. They **are wearing** paper hats. Elaine is very happy. She **is smiling**.