There are a few grammar differences between British and American English. I will cover the two most significant
ones.

When Americans create sentences using ‘just’, ‘already’, or ‘yet’, they generally use the past simple tense, but in
the UK, people use the present perfect.

So an American, for instances, could say:

“She already went home.”
“She didn’t arrive yet.”

And the British may say:

“I’ve already had my tea and biscuits.”
 Or “She hasn’t arrived yet.”

These two methods both mean the same thing with just a small grammatical difference.

The differences in vocabulary between American and British English are larger than the grammatical differences.
But these are usually not a problem. Most of the vocabulary differences are with informal speech and slang.

Many Americans wouldn’t know the British slang ‘naff’, which means ‘un-cool’ or ‘poor-quality’. In American
English people would use ‘wack’ instead.
“This coffee is wack.  It tastes like it was made yesterday.”

Another instance of these differences would be:

In Britain, if we wanted to say 2:45 then we would say:
“Quarter to three”, or 3:15 would be “Quarter past three”.

While in America we would say:
“Quarter after three” for 3:15.

It’s a minor difference but one that doesn’t cause problems for comprehension. Spelling between American and
British English does also have some difference.

One example is the word “practice” as a verb:

In British English, we would spell this with an ‘s’ so:
PractiSe

But in American English, it’s spelled with a c at the end:
PractiCe