Adverbial clauses and phrases that begin a sentence are usually set off with commas.

• Having made that decision, we turned our attention to other matters.
• In order to receive a high school diploma, a student must earn 16 credits from public or private secondary schools.
  
• In addition, staff members respond to queries, take new orders, and initiate billing.

If the sentence can be easily read without a comma, the comma may be omitted. The phrase will usually be short—four words or less—but even after a longer phrase the comma is often omitted.

• As cars age, they depreciate.
  

or

• As cars age they depreciate.
  

• In January the firm will introduce a new line of investigative services.
  
• On the map the town appeared as a small dot in the midst of vast emptiness.
  
• If nobody comes forward by Friday I will have to take further steps.
  

Adverbial clauses and phrases that introduce a main clause other than the first main clause are usually set off with commas. If the clause or phrase follows a conjunction, one comma often precedes  the conjunction and one follows the clause or phrase.

Alternatively, one comma precedes the conjunction and two more enclose the clause or phrase, or a single comma precedes the conjunction. Short phrases, and phrases in short sentences, tend not to be enclosed in commas.

• They have redecorated the entire store, but[,] to the delight of their customers, it retains much of its original flavor.
  
• We haven't left Springfield yet, but when we get to Boston we'll call you.
  

A comma is not used after an introductory phrase if the phrase immediately precedes the main verb.

• From the next room came a loud expletive.

A subordinate clause or phrase that modifies a noun is not set off by commas if it is restrictive (or essential)—that is, if its removal would alter the noun's meaning.

• The man who wrote this obviously had no firsthand knowledge of the situation.
  
• They entered through the first door that wasn't locked.
  

If the meaning would not be altered by its removal, the clause or phrase is considered nonrestrictive (or nonessential) and usually is set off by commas.

• The new approach, which was based on team teaching, was well received.
  
• Wechsler, who has done solid reporting from other battlefronts, is simply out of his depth here.
  
• They tried the first door, which led nowhere.
  

Commas set off an adverbial clause or phrase that falls between the subject and the verb.

• The Clapsaddle sisters, to keep up appearances, rode to the park every Sunday in their rented carriage.

Commas set off modifying phrases that do not immediately precede the word or phrase they modify.

• Scarbo, intent as usual on his next meal, was snuffling around the butcher's bins.
  
• The negotiators, tired and discouraged, headed back to the hotel.
  
• We could see the importance, both long-term and short-term, of her proposal.
  

An absolute phrase (a participial phrase with its own subject that is grammatically independent of the rest of the sentence) is set off with commas.

• Our business being concluded, we adjourned for refreshments.
  
• We headed southward, the wind freshening behind us, to meet the rest of the fleet in the morning.
  
• I'm afraid of his reaction, his temper being what it is.