The perfect aspect
In American English it is very common to use the simple past tense instead of the present perfect which speakers of British English might use.

American English 
I feel tired. I worked too much. I think I lost my keys. Did you see them anywhere?
Are you going to the show? No I already went.
You're looking for Jane. I just spoke to her.

British English
I feel tired. I've worked too much. I think I've lost my keys. Have you seen them anywhere?
Are you going to the show? No I've already gone.
You’re looking for Jane. I've just spoken to her.

Have or Take
In British English, the verb 'have' is used in sentences with certain objects. (The verb is used in a context where it has very little meaning but explains the action.
I need to have a bath. He's having a rest.
In American English 'take' is used instead of have:
He's taking a shower. Let's take a break.

Verbs with collective nouns
In British English certain collective nouns can have both a plural and a singular verb:
The team is walking onto the field. The team are walking onto the field.
In British English both 'is' or 'are' can be correct depending on whether the team is referred to as a group or individually. 
However in American English only the singular is used:

Auxiliary and modal verbs
In British English 'needn't' is often used instead of 'don't need to', e.g.:
They needn’t stay longer. They can leave.
They don’t need to stay longer. They can leave.
In American English ‘needn’t’ is unusual.

Shall/should
In British English          In American English
Should we go?               Shall we go?

On/at/in
In British English:                In American English:
At the weekend.                    On the weekend
At university                           In high school/In university
Different to/from                    Different from/than
Write to                                 Write
Write to me when you can    Write me when you can

Past tense forms
Some past tenses and past participles are different in British and American English. The most common is got. 'Have got' is used in American English but only to mean 'have'. 'Gotten' is the past participle of 'get' in American English.

British English              American English
You’ve got taller.            You’ve gotten taller.

You've got a car.            You've got a car. – (You have a car.)

Note:
Although these differences have been pointed out it is important to understand that not all American native speakers of English use these differences. It is also important to realise that one type of English is not better than another. They are both valid. It is important however to be aware of these differences. When writing for exams etc., it's important to be consistent with which English you use.

Lesson by Tristan

Decide which of these sentences is most likely to be American or British English:

• 1. It’s gotten harder to find a job these days.
   
  American
  British
  
  
• 2. I’ve just finished the report.
   
  British
  American
  
  
• 3. I’ll meet her on the weekend.
   
  American
  British
  
  
• 4. You needn’t come if you don’t want to.
  
  British
  American
  
  
• 5. He's taking a rest right now.
  
  British
  American
  
  
• 6. I already saw this movie. What do you think of it?
  
  British
  American
  
  
• 7. I haven’t yet told him about his promotion.
  
  British
  American
  
  
• 8. Paris is very different than London.
  
  British
  American
  
  
• 9. I didn’t make many friends in university. I was studying too hard.
  
  American
  British
  
  
• 10. The team was each given a prize.
  
  British
  American