Below are some expressions and wording patterns you might look for in your drafts if you are trying to reduce wordiness.

Wordy phrase	Revision
At this point in time	Now
In the event that	If
It is believed by many that	Many believe [notice you can often just delete the it is…that construction]
In order to	To
Make an effort to	Try to
There is. . .that	[just delete these words usually]

Below are some empty phrases and suggestions for fixing them.

Empty word or phrase	Wordy Example	Revision
Because of the fact that	Because of the fact that a special exhibit is scheduled, the museum will be open until 10 p.m.	Because of a special exhibit, the museum will be open until 10 p.m.
For the purpose of	Work crews were dispatched for the purpose of fixing potholes.	Work crews were dispatched to fix the potholes.
In light of the fact that	In light of the fact that the rainfall was so heavy, we had flooding.	Because the rainfall was so heavy, we had flooding.
Have a tendency to	The team had a tendency to lose home games.	The team often lost home games.
That exists	The crime rate that exists is unacceptable.	The crime rate is unacceptable.

To reduce wordiness, see whether you can reduce clauses sometimes:

The Titanic, which was a huge ocean liner, sank in 1912. The Titanic, a huge ocean liner, sank in 1912.

You could also look at ways to eliminate phrases by moving key information from the phrase into another part of the sentence:

Although loaded with luxuries, the liner was thought to be unsinkable.
The luxury liner was thought to be unsinkable.